Journal of Algebraic Geometry最新文献

{"title":"Equivariant connective 𝐾-theory","authors":"N. Karpenko, A. Merkurjev","doi":"10.1090/jag/773","DOIUrl":"https://doi.org/10.1090/jag/773","url":null,"abstract":"For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theory mapping to the equivariant \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-homology of Guillot and the equivariant algebraic \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41383881","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":"Chow dilogarithm and strong Suslin reciprocity law","authors":"V. Bolbachan","doi":"10.1090/jag/811","DOIUrl":"https://doi.org/10.1090/jag/811","url":null,"abstract":"We prove a conjecture of A. Goncharov concerning strong Suslin reciprocity law. The main idea of the proof is the construction of the norm map on so-called lifted reciprocity maps. This construction is similar to the construction of the norm map on Milnor \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-theory. As an application, we express Chow dilogarithm in terms of Bloch-Wigner dilogarithm. Also, we obtain a new reciprocity law for four rational functions on an arbitrary algebraic surface with values in the pre-Bloch group.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45793528","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":"Applications of a Grassmannian technique to hyperbolicity, Chow equivalency, and Seshadri constants","authors":"Eric Riedl, David H Yang","doi":"10.1090/JAG/786","DOIUrl":"https://doi.org/10.1090/JAG/786","url":null,"abstract":"In this paper we further develop a Grassmannian technique used to prove results about very general hypersurfaces and present three applications. First, we provide a short proof of the Kobayashi conjecture given previously established results on the Green–Griffiths–Lang conjecture. Second, we completely resolve a conjecture of Chen, Lewis, and Sheng on the dimension of the space of Chow-equivalent points on a very general hypersurface, proving the remaining cases and providing a short, alternate proof for many of the previously known cases. Finally, we relate Seshadri constants of very general points to Seshadri constants of arbitrary points of very general hypersurfaces.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43567961","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":"Global rigidity of the period mapping","authors":"B. Farb","doi":"10.1090/jag/809","DOIUrl":"https://doi.org/10.1090/jag/809","url":null,"abstract":"<p>Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M Subscript g comma n\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">{mathcal M}_{g,n}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> denote the moduli space of smooth, genus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ggeq 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> curves with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than-or-equal-to 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ngeq 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> marked points. Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper A Subscript h\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">A</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:mi>h</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">{mathcal A}_h</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> denote the moduli space of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"h\">\u0000 <mml:semantics>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">h</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-dimensional, principally polarized abelian varieties. Let <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g greater-than-or-equal-to 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ggeq 3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"h less-than-or-equal-to g\">\u0000 <mml:semantics>\u0000 ","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46369246","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":"Zariski’s dimensionality type of singularities. Case of dimensionality type 2","authors":"A. Parusiński, L. Paunescu","doi":"10.1090/jag/815","DOIUrl":"https://doi.org/10.1090/jag/815","url":null,"abstract":"In the 1970s O. Zariski introduced a general theory of equisingularity for algebroid and algebraic hypersurfaces over an algebraically closed field of characteristic zero. His theory builds up on understanding the dimensionality type of hypersurface singularities, notion defined recursively by considering the discriminants loci of successive “generic” corank \u0000\u0000 \u0000 1\u0000 1\u0000 \u0000\u0000 projections. The theory of singularities of dimensionality type 1, that is the ones appearing generically in codimension 1, was developed by Zariski in his foundational papers on equisingular families of plane curve singularities. In this paper we completely settle the case of dimensionality type 2, by studying Zariski equisingular families of surfaces singularities, not necessarily isolated, in the three-dimensional space.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49144330","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":"The Chow rings of the moduli spaces of curves of genus 7, 8, and 9","authors":"Samir Canning, H. Larson","doi":"10.1090/jag/818","DOIUrl":"https://doi.org/10.1090/jag/818","url":null,"abstract":"<p>The rational Chow ring of the moduli space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M Subscript g\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>g</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {M}_g</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of curves of genus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\">\u0000 <mml:semantics>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">g</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is known for <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g less-than-or-equal-to 6\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>g</mml:mi>\u0000 <mml:mo>≤<!-- ≤ --></mml:mo>\u0000 <mml:mn>6</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">g leq 6</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Here, we determine the rational Chow rings of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M 7 comma script upper M 8\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>7</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>8</mml:mn>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {M}_7, mathcal {M}_8</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M 9\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>9</mml:mn>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {M}_9</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> by showing they are tautological. The key ingredient is intersection theory on Hurwitz spaces of degree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4\">\u0000 <mml:semantics>\u0000 <mml:mn>4</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">4</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" al","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44753557","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":"Equations for a K3 Lehmer map","authors":"Simon Brandhorst, N. Elkies","doi":"10.1090/jag/810","DOIUrl":"https://doi.org/10.1090/jag/810","url":null,"abstract":"C. T. McMullen proved the existence of a K3 surface with an automorphism of entropy given by the logarithm of Lehmer’s number, which is the minimum possible among automorphisms of complex surfaces. We reconstruct equations for the surface and its automorphism from the Hodge theoretic model provided by McMullen. The approach is computer aided and relies on finite non-symplectic automorphisms, \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000-adic lifting, elliptic fibrations and the Kneser neighbor method for \u0000\u0000 \u0000 \u0000 Z\u0000 \u0000 mathbb {Z}\u0000 \u0000\u0000-lattices. It can be applied to reconstruct any automorphism of an elliptic K3 surface from its action on the Neron-Severi lattice.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2021-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41939634","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":"Localizing virtual cycles for Donaldson-Thomas invariants of Calabi-Yau 4-folds","authors":"Y. Kiem, Hyeonjun Park","doi":"10.1090/jag/816","DOIUrl":"https://doi.org/10.1090/jag/816","url":null,"abstract":"<p>In 2020, Oh and Thomas constructed a virtual cycle <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket upper X right-bracket Superscript normal v normal i normal r Baseline element-of upper A Subscript asterisk Baseline left-parenthesis upper X right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:msup>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">v</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">i</mml:mi>\u0000 <mml:mi mathvariant=\"normal\">r</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\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\">[X]^{mathrm {vir}} in A_*(X)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for a quasi-projective moduli space <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> of stable sheaves or complexes over a Calabi-Yau 4-fold against which DT4 invariants may be defined as integrals of cohomology classes. In this paper, we prove that the virtual cycle localizes to the zero locus <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X left-parenthesis sigma right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>σ<!-- σ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">X(sigma )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of an isotropic cosection <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"sigma\">\u0000 <mml:semantics>\u0000 <mml:mi>σ<!-- σ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">sigma</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the obstruction sheaf <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O b Subscript upper X\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:msub>\u0000 <mml:mi>b</mml:mi>\u0000 <mml:mi>X</mml:mi>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ob_X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <inline-formula conten","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48281262","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":"Minimal model program for semi-stable threefolds in mixed characteristic","authors":"Teppei Takamatsu, Shou Yoshikawa","doi":"10.1090/jag/813","DOIUrl":"https://doi.org/10.1090/jag/813","url":null,"abstract":"<p>In this paper, we study the minimal model theory for threefolds in mixed characteristic. As a generalization of a result of Kawamata, we show that the minimal model program (MMP) holds for strictly semi-stable schemes over an excellent Dedekind scheme <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\">\u0000 <mml:semantics>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">V</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of relative dimension two without any assumption on the residue characteristics of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\">\u0000 <mml:semantics>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">V</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We also prove that we can run a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper K Subscript upper X slash upper V Baseline plus normal upper Delta right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>V</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(K_{X/V}+Delta )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-MMP over <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z\">\u0000 <mml:semantics>\u0000 <mml:mi>Z</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Z</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi colon upper X right-arrow upper Z\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>π<!-- π --></mml:mi>\u0000 <mml:mo>:<!-- : --></mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mi>Z</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">pi colon X to Z</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a projective birational morphism of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Q}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-factor","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60551334","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":"Elliptic zastava","authors":"M. Finkelberg, M. Matviichuk, A. Polishchuk","doi":"10.1090/jag/803","DOIUrl":"https://doi.org/10.1090/jag/803","url":null,"abstract":"We study the elliptic zastava spaces, their versions (twisted, Coulomb, Mirković local spaces, reduced) and relations with monowalls moduli spaces and Feigin-Odesskiĭ moduli spaces of \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000-bundles with parabolic structure on an elliptic curve.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45663622","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}