Journal of Algebraic Geometry最新文献

{"title":"Projective manifolds whose tangent bundle contains a strictly nef subsheaf","authors":"Jie Liu, Wenhao Ou, Xiaokui Yang","doi":"10.1090/jag/807","DOIUrl":"https://doi.org/10.1090/jag/807","url":null,"abstract":"<p>Suppose that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a projective manifold whose tangent bundle <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Subscript upper X\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mi>X</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">T_X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> contains a locally free strictly nef subsheaf. We prove that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is isomorphic to either a projective space or a projective bundle over a hyperbolic manifold of general type. Moreover, if the fundamental group <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi 1 left-parenthesis upper X right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>π<!-- π --></mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">pi _1(X)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is virtually solvable, then <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is isomorphic to a projective space.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43641826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A codimension 2 component of the Gieseker-Petri locus","authors":"Margherita Lelli–Chiesa","doi":"10.1090/jag/780","DOIUrl":"https://doi.org/10.1090/jag/780","url":null,"abstract":"<p>We show that the Brill-Noether locus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Subscript 18 comma 16 Superscript 3\">\u0000 <mml:semantics>\u0000 <mml:msubsup>\u0000 <mml:mi>M</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>18</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>16</mml:mn>\u0000 </mml:mrow>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msubsup>\u0000 <mml:annotation encoding=\"application/x-tex\">M^3_{18,16}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is an irreducible component of the Gieseker-Petri locus in genus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"18\">\u0000 <mml:semantics>\u0000 <mml:mn>18</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">18</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> having codimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the moduli space of curves. This result disproves a conjecture predicting that the Gieseker-Petri locus is always divisorial.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47940720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Codimension two integral points on some rationally connected threefolds are potentially dense","authors":"David McKinnon, Mike Roth","doi":"10.1090/jag/782","DOIUrl":"https://doi.org/10.1090/jag/782","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be a smooth, projective, rationally connected variety, defined over a number field &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;k&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;k&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, and let &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z subset-of upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mi&gt;Z&lt;/mml:mi&gt;\u0000 &lt;mml:mo&gt;⊂&lt;!-- ⊂ --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Zsubset X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be a closed subset of codimension at least two. In this paper, for certain choices of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, we prove that the set of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;Z&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Z&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-integral points is potentially Zariski dense, in the sense that there is a finite extension &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper K\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;K&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;K&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;k&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;k&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; such that the set of points &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper P element-of upper X left-parenthesis upper K right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mi&gt;P&lt;/mml:mi&gt;\u0000 &lt;mml:mo&gt;∈&lt;!-- ∈ --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;K&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Pin X(K)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; that are &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math x","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48063382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the monodromy group of desingularised moduli spaces of sheaves on K3 surfaces","authors":"C. Onorati","doi":"10.1090/jag/802","DOIUrl":"https://doi.org/10.1090/jag/802","url":null,"abstract":"In this paper we prove a conjecture of Markman about the shape of the monodromy group of irreducible holomorphic symplectic manifolds of OG10 type. As a corollary, we also compute the locally trivial monodromy group of the underlying singular symplectic variety.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49367741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bloch’s formula for 0-cycles with modulus and higher-dimensional class field theory","authors":"F. Binda, A. Krishna, S. Saito","doi":"10.1090/jag/792","DOIUrl":"https://doi.org/10.1090/jag/792","url":null,"abstract":"<p>We prove Bloch’s formula for the Chow group of 0-cycles with modulus on a smooth quasi-projective surface over a field. We use this formula to give a simple proof of the rank one case of a conjecture of Deligne and Drinfeld on lisse <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q overbar Subscript script l\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mover>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo accent=\"false\">¯<!-- ¯ --></mml:mo>\u0000 </mml:mover>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>ℓ<!-- ℓ --></mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">overline {mathbb {Q}}_{ell }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-sheaves. This was originally solved by Kerz and Saito in characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"not-equals 2\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo>≠<!-- ≠ --></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">neq 2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44914700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tropical floor plans and enumeration of complex and real multi-nodal surfaces","authors":"H. Markwig, Thomas Markwig, Kristin M. Shaw, E. Shustin","doi":"10.1090/jag/774","DOIUrl":"https://doi.org/10.1090/jag/774","url":null,"abstract":"&lt;p&gt;The family of complex projective surfaces in &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P cubed\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;3&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^3&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; of degree &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;d&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;d&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; having precisely &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;δ&lt;!-- δ --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;delta&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; nodes as their only singularities has codimension &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"delta\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;δ&lt;!-- δ --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;delta&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; in the linear system &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue script upper O Subscript double-struck upper P cubed Baseline left-parenthesis d right-parenthesis EndAbsoluteValue\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:msub&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\"&gt;O&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;3&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:msub&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;d&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;|&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;|{mathcal O}_{mathbb {P}^3}(d)|&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; for sufficiently large &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;d&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;d&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:mat","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49598659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Eigenvalues and dynamical degrees of self-maps on abelian varieties","authors":"Fei Hu","doi":"10.1090/jag/806","DOIUrl":"https://doi.org/10.1090/jag/806","url":null,"abstract":"&lt;p&gt;Let &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be a smooth projective variety over an algebraically closed field, and &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon upper X right-arrow upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mi&gt;f&lt;/mml:mi&gt;\u0000 &lt;mml:mo&gt;:&lt;!-- : --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;→&lt;!-- → --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;fcolon Xto X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; a surjective self-morphism of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;X&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;X&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;. The &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"i\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;i&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;i&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-th cohomological dynamical degree &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"chi Subscript i Baseline left-parenthesis f right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:msub&gt;\u0000 &lt;mml:mi&gt;χ&lt;!-- χ --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:mi&gt;i&lt;/mml:mi&gt;\u0000 &lt;/mml:msub&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;f&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;chi _i(f)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is defined as the spectral radius of the pullback &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f Superscript asterisk\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mi&gt;f&lt;/mml:mi&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mo&gt;∗&lt;!-- ∗ --&gt;&lt;/mml:mo&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;f^{*}&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; on the étale cohomology group &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Subscript ModifyingAbove normal e With acute normal t Superscript i Baseline left-parenthesis upper X comma bold upper Q Subscript script l Baseline right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:msubsup&gt;\u0000 &lt;mml:mi&gt;H&lt;/mml:mi&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:move","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46819321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extension of cohomology classes and holomorphic sections defined on subvarieties","authors":"Xiangyu Zhou, Langfeng Zhu","doi":"10.1090/JAG/766","DOIUrl":"https://doi.org/10.1090/JAG/766","url":null,"abstract":"In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answer to a question posed by Cao-Demailly-Matsumura and unifies a few well-known injectivity theorems. The second result generalizes and optimizes a general \u0000\u0000 \u0000 \u0000 L\u0000 2\u0000 \u0000 L^2\u0000 \u0000\u0000 extension theorem obtained by Demailly.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43104787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scattering diagrams, stability conditions, and coherent sheaves on ℙ²","authors":"Pierrick Bousseau","doi":"10.1090/jag/795","DOIUrl":"https://doi.org/10.1090/jag/795","url":null,"abstract":"&lt;p&gt;We show that a purely algebraic structure, a two-dimensional scattering diagram, describes a large part of the wall-crossing behavior of moduli spaces of Bridgeland semistable objects in the derived category of coherent sheaves on &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;2&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^2&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;. This gives a new algorithm computing the Hodge numbers of the intersection cohomology of the classical moduli spaces of Gieseker semistable sheaves on &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;2&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^2&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, or equivalently the refined Donaldson-Thomas invariants for compactly supported sheaves on local &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;2&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^2&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;.&lt;/p&gt;\u0000\u0000&lt;p&gt;As applications, we prove that the intersection cohomology of moduli spaces of Gieseker semistable sheaves on &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P squared\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;P&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mn&gt;2&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {P}^2&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is Hodge-Tate, and we give the first non-trivial numerical checks of the general &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"chi\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;χ&lt;!-- χ --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;chi&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-independence conjecture for refined Donaldson-Thomas invariants of one-dimensional sheaves on local &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathM","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45036037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “A flexible affine 𝑀-sextic which is algebraically unrealizable”","authors":"S. F. Touzé, S. Orevkov, E. Shustin","doi":"10.1090/jag/733","DOIUrl":"https://doi.org/10.1090/jag/733","url":null,"abstract":"We prove the algebraic unrealizability of a certain isotopy type of plane affine real algebraic \u0000\u0000 \u0000 M\u0000 M\u0000 \u0000\u0000-sextic which is pseudoholomorphically realizable. This result completes the classification up to isotopy of real algebraic affine \u0000\u0000 \u0000 M\u0000 M\u0000 \u0000\u0000-sextics. The proof of this result given in a previous paper by the first two authors [J. Algebraic Geom. 11 (2002), pp. 293–310] was incorrect.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/733","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46065596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}