Journal of Algebraic Geometry最新文献

{"title":"The class of the affine line is a zero divisor in the Grothendieck ring","authors":"L. Borisov","doi":"10.7282/T33B62H9","DOIUrl":"https://doi.org/10.7282/T33B62H9","url":null,"abstract":"","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"28 3 1","pages":"203-209"},"PeriodicalIF":1.8,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78792507","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":"Algebraic approximations of fibrations in abelian varieties over a curve","authors":"Hsueh-Yung Lin","doi":"10.1090/jag/791","DOIUrl":"https://doi.org/10.1090/jag/791","url":null,"abstract":"<p>For every fibration <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon upper X right-arrow upper B\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>:</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mi>B</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f : X to B</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with <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> a compact Kähler manifold, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B\">\u0000 <mml:semantics>\u0000 <mml:mi>B</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">B</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> a smooth projective curve, and a general fiber of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\u0000 <mml:semantics>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> an abelian variety, we prove that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\u0000 <mml:semantics>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has an algebraic approximation.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60551290","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":"Diagonalisable $p$-groups cannot fix exactly one point on projective varieties","authors":"Olivier Haution","doi":"10.1090/jag/749","DOIUrl":"https://doi.org/10.1090/jag/749","url":null,"abstract":"We prove an algebraic version of classical theorem in topology, asserting that an abelian p-group action on a smooth projective variety of positive dimension cannot fix exactly one point. When the group has only two elements, we prove that the number of fixed points cannot be odd. The main tool is a construction originally used by Rost in the context of the degree formula. The framework of diagonalisable groups allows us to include the case of base fields of characteristic p.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/749","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550964","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":"Images of manifolds with semi-ample anti-canonical divisor","authors":"C. Birkar, Yifei Chen","doi":"10.1090/JAG/662","DOIUrl":"https://doi.org/10.1090/JAG/662","url":null,"abstract":"We prove that if f : X → Z is a smooth surjective morphism between projective manifolds and if −KX is semi-ample, then −KZ is also semi-ample. This was conjectured by Fujino and Gongyo. We list several counter-examples to show that this fails without the smoothness assumption on f . We prove the above result by proving some results concerning the moduli divisor of the canonical bundle formula associated to a klt-trivial fibration (X,B)→ Z.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"10 1","pages":"273-287"},"PeriodicalIF":1.8,"publicationDate":"2016-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/662","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550551","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":"Gorenstein modifications and mathds{𝑄}-Gorenstein rings","authors":"Hailong Dao, O. Iyama, Ryo Takahashi, M. Wemyss","doi":"10.1090/JAG/760","DOIUrl":"https://doi.org/10.1090/JAG/760","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 R\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;R&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;R&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be a Cohen–Macaulay normal domain with a canonical module &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"omega Subscript upper R\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:msub&gt;\u0000 &lt;mml:mi&gt;ω&lt;!-- ω --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:mi&gt;R&lt;/mml:mi&gt;\u0000 &lt;/mml:msub&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;omega _R&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;. It is proved that if &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;R&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;R&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; admits a noncommutative crepant resolution (NCCR), then necessarily it is &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 Q\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;Q&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathds {Q}&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;-Gorenstein. Writing &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;S&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;S&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; for a Zariski local canonical cover of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;R&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;R&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, a tight relationship between the existence of noncommutative (crepant) resolutions on &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper R\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;R&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;R&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;S&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;S&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is given. A weaker notion of Gorenstein modification is developed, and a similar tight relationship is given. There are three applications: non-Gorenstein quotient singularities by connected reductive groups cannot admit an NCCR, the centre of any NCCR is log-termin","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/760","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60551255","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":"Spaces with 𝔾_{𝕞}-action, hyperbolic localization and nearby cycles","authors":"Timo Richarz","doi":"10.1090/jag/710","DOIUrl":"https://doi.org/10.1090/jag/710","url":null,"abstract":"We study families of algebraic spaces with \u0000\u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 m\u0000 \u0000 {mathbb G}_m\u0000 \u0000\u0000-action and prove Braden’s theorem on hyperbolic localization for arbitrary base schemes. As an application, we obtain that hyperbolic localization commutes with nearby cycles.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/710","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550443","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":"Algebraic stratified general position and transversality","authors":"C. McCrory, A. Parusiński, L. Paunescu","doi":"10.1090/JAG/713","DOIUrl":"https://doi.org/10.1090/JAG/713","url":null,"abstract":"The method of Whitney interpolation is used to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for semialgebraic subsets.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/713","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550938","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 plane valuations","authors":"C. Galindo, F. Monserrat, Julio Jos'e Moyano-Fern'andez","doi":"10.1090/JAG/722","DOIUrl":"https://doi.org/10.1090/JAG/722","url":null,"abstract":"&lt;p&gt;We consider the value &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"ModifyingAbove mu With caret left-parenthesis nu right-parenthesis equals limit Underscript m right-arrow normal infinity Endscripts m Superscript negative 1 Baseline a left-parenthesis m upper L right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mover&gt;\u0000 &lt;mml:mi&gt;μ&lt;!-- μ --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;^&lt;!-- ^ --&gt;&lt;/mml:mo&gt;\u0000 &lt;/mml:mover&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;ν&lt;!-- ν --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt;\u0000 &lt;mml:mo&gt;=&lt;/mml:mo&gt;\u0000 &lt;mml:munder&gt;\u0000 &lt;mml:mo movablelimits=\"true\" form=\"prefix\"&gt;lim&lt;/mml:mo&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi&gt;m&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;→&lt;!-- → --&gt;&lt;/mml:mo&gt;\u0000 &lt;mml:mi mathvariant=\"normal\"&gt;∞&lt;!-- ∞ --&gt;&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:munder&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mi&gt;m&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:mn&gt;1&lt;/mml:mn&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:mi&gt;a&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;m&lt;/mml:mi&gt;\u0000 &lt;mml:mi&gt;L&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;hat {mu } (nu ) = lim _{m rightarrow infty } m^{-1} a(mL)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, where &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"a left-parenthesis m upper L right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mi&gt;a&lt;/mml:mi&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;m&lt;/mml:mi&gt;\u0000 &lt;mml:mi&gt;L&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;a(mL)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is the last value of the vanishing sequence of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H Superscript 0 Baseline left-parenthesis m upper L right-parenthesis\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mi&gt;H&lt;/mml:mi&gt;\u0000 &lt;mml:mn&gt;0&lt;/mml:mn&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:mi&gt;m&lt;/mml:mi&gt;\u0000 &lt;mml:mi&gt;L&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;H^0(mL)&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; along a divisorial or irrational valuation &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"nu\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;ν&lt;!-- ν --&gt;&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;nu&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/m","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/722","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550949","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":"Uniqueness of embeddings of the affine line into algebraic groups","authors":"P. Feller, Immanuel Stampfli","doi":"10.1090/JAG/725","DOIUrl":"https://doi.org/10.1090/JAG/725","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 Y\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;Y&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Y&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; be the underlying variety of a complex connected affine algebraic group. We prove that two embeddings of the affine line &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 C\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;mathbb {C}&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; into &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;Y&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Y&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; are the same up to an automorphism of &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;Y&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Y&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; provided that &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mi&gt;Y&lt;/mml:mi&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;Y&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; is not isomorphic to a product of a torus &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis double-struck upper C Superscript asterisk Baseline right-parenthesis Superscript k\"&gt;\u0000 &lt;mml:semantics&gt;\u0000 &lt;mml:mrow&gt;\u0000 &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt;\u0000 &lt;mml:msup&gt;\u0000 &lt;mml:mrow class=\"MJX-TeXAtom-ORD\"&gt;\u0000 &lt;mml:mi mathvariant=\"double-struck\"&gt;C&lt;/mml:mi&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:mo&gt;∗&lt;!-- ∗ --&gt;&lt;/mml:mo&gt;\u0000 &lt;/mml:msup&gt;\u0000 &lt;mml:msup&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:msup&gt;\u0000 &lt;/mml:mrow&gt;\u0000 &lt;mml:annotation encoding=\"application/x-tex\"&gt;(mathbb {C}^ast )^k&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt; and one of the three varieties &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 C 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;C&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 {C}^3&lt;/mml:annotation&gt;\u0000 &lt;/mml:semantics&gt;\u0000&lt;/mml:math&gt;\u0000&lt;/inline-formula&gt;, &lt;inline-formula content-type=\"math/mathml\"&gt;\u0000&lt;mml:m","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/725","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60551031","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":"Stable rationality of orbifold Fano 3-fold hypersurfaces","authors":"Takuzo Okada","doi":"10.1090/JAG/712","DOIUrl":"https://doi.org/10.1090/JAG/712","url":null,"abstract":"<p>We determine the rationality of very general quasi-smooth Fano <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-fold weighted hypersurfaces completely and determine the stable rationality of them except for cubic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-folds. More precisely we prove that (i) very general Fano <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-fold weighted hypersurfaces of index <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"1\">\u0000 <mml:semantics>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or <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> are not stably rational except possibly for the cubic 3-folds, (ii) among the <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"27\">\u0000 <mml:semantics>\u0000 <mml:mn>27</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">27</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> families of Fano 3-fold weighted hypersurfaces of index greater than <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>, very general members of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"7\">\u0000 <mml:semantics>\u0000 <mml:mn>7</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">7</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> specific families are not stably rational, and the remaining <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"20\">\u0000 <mml:semantics>\u0000 <mml:mn>20</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">20</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> families consist of rational varieties.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2016-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/712","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60550485","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}