We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of two operations: one interchanges a quadric hypersurface with its classical projective dual and the other interchanges a quadric hypersurface with the double cover branched along it.
{"title":"Homological projective duality for quadrics","authors":"A. Kuznetsov, Alexander Perry","doi":"10.1090/JAG/767","DOIUrl":"https://doi.org/10.1090/JAG/767","url":null,"abstract":"We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of two operations: one interchanges a quadric hypersurface with its classical projective dual and the other interchanges a quadric hypersurface with the double cover branched along it.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2019-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48760564","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}
Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic p p , the higher direct images of an overconvergent F F -isocrystal are overconvergent F F -isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove the Künneth formula for the crystalline fundamental group scheme.
{"title":"A crystalline incarnation of Berthelot’s conjecture and Künneth formula for isocrystals","authors":"V. D. Proietto, F. Tonini, Lei Zhang","doi":"10.1090/jag/789","DOIUrl":"https://doi.org/10.1090/jag/789","url":null,"abstract":"Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic \u0000\u0000 \u0000 p\u0000 p\u0000 \u0000\u0000, the higher direct images of an overconvergent \u0000\u0000 \u0000 F\u0000 F\u0000 \u0000\u0000-isocrystal are overconvergent \u0000\u0000 \u0000 F\u0000 F\u0000 \u0000\u0000-isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove the Künneth formula for the crystalline fundamental group scheme.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45766738","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}
<p>We consider <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu Subscript p"> <mml:semantics> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">mu _p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>- and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha Subscript p"> <mml:semantics> <mml:msub> <mml:mi>α<!-- α --></mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">alpha _p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p greater-than 0"> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">p > 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu Subscript p"> <mml:semantics> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">mu _p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>- and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha Subscript p"> <mml:semantics> <mml:msub> <mml:mi>α<!-- α --></mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">alpha _p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-actions are analogous to those of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper Z slash l double-struck upper Z"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>l</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">mathbb {Z}/lmathbb {Z}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-actions (for primes <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="l not-equals p"> <mml:semantics> <mml:mrow> <mml:mi>l</mml:m
我们考虑μ p mu ＿p -和α p alpha ＿p -作用在特征p > 0 p > 0的RDP K3曲面(允许有有理双点(RDP)奇点的K3曲面)上。我们研究可能的特征，商曲面和商奇点。结果表明，μ p mu ＿p -和α p alpha ＿p -作用的这些性质类似于Z/l Z mathbb Z{/l }mathbb Z{ -作用(对于素数l≠p l }neq p)和Z/p Z mathbb Z{/p分别为}mathbb Z{商。相反地，我们还证明了具有一定奇异位形的RDP K3曲面允许μ p }mu ＿p -或α p alpha ＿p -或Z/p Z mathbb Z{/p }mathbb Z{ -被“类K3”曲面覆盖，该曲面通常是RDP K3曲面，但并不总是这样。就像特征22中Enriques曲面的典型覆盖一样。}
{"title":"𝜇_{𝑝}- and 𝛼_{𝑝}-actions on K3 surfaces in characteristic 𝑝","authors":"Y. Matsumoto","doi":"10.1090/jag/804","DOIUrl":"https://doi.org/10.1090/jag/804","url":null,"abstract":"<p>We consider <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu Subscript p\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>μ<!-- μ --></mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mu _p</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=\"alpha Subscript p\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha _p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p > 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"mu Subscript p\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>μ<!-- μ --></mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">mu _p</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=\"alpha Subscript p\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha _p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-actions are analogous to those of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Z slash l double-struck upper Z\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Z</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>l</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Z</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Z}/lmathbb {Z}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-actions (for primes <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"l not-equals p\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>l</mml:m","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47964130","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}
Atsushi Ito, Makoto Miura, Shinnosuke Okawa, K. Ueda
Motivated by [J. Algebraic Geom. 27 (2018), pp. 203–209] and [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 936–939], we show the equality ([X]−[Y])⋅[A1]=0left ( [ X ] - [ Y ] right ) cdot [ mathbb {A} ^{ 1 } ] = 0 in the Grothendieck ring of varieties, where (X,Y)( X, Y ) is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type G2G _{ 2 }.
[J]代数几何，27 (2018)，pp. 203-209 [j]。r .数学。学会科学。(Paris 354 (2016)， pp. 936-939)，我们证明了在Grothendieck环上的等式([X]−[Y])⋅[A 1] = 0 left ([X] - [Y] right) cdot [mathbb {A} ^{1}] = 0，其中(X, Y) (X，Y)是一对从G 2 G _{2}型格拉斯曼人身上剪下来的卡拉比-丘三褶。
{"title":"The class of the affine line is a zero divisor in the Grothendieck ring: Via 𝐺₂-Grassmannians","authors":"Atsushi Ito, Makoto Miura, Shinnosuke Okawa, K. Ueda","doi":"10.1090/JAG/731","DOIUrl":"https://doi.org/10.1090/JAG/731","url":null,"abstract":"<p>Motivated by [J. Algebraic Geom. 27 (2018), pp. 203–209] and [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 936–939], we show the equality <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis left-bracket upper X right-bracket minus left-bracket upper Y right-bracket right-parenthesis dot left-bracket double-struck upper A Superscript 1 Baseline right-bracket equals 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow>\u0000 <mml:mo>(</mml:mo>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>Y</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo>)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mo>⋅<!-- ⋅ --></mml:mo>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">A</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">left ( [ X ] - [ Y ] right ) cdot [ mathbb {A} ^{ 1 } ] = 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the Grothendieck ring of varieties, where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis upper X comma upper Y right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>Y</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">( X, Y )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G 2\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">G _{ 2 }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/731","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60551171","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}
In the present paper, we consider the pseudo-effective line bundles over holomorphically convex manifolds and obtain some results related to the vanishing, finiteness, and surjectivity of analytic cohomology groups with multiplier ideal sheaves.
{"title":"Pseudo-effective line bundles over holomorphically convex manifolds","authors":"Xiankui Meng, Xiangyu Zhou","doi":"10.1090/JAG/714","DOIUrl":"https://doi.org/10.1090/JAG/714","url":null,"abstract":"In the present paper, we consider the pseudo-effective line bundles over holomorphically convex manifolds and obtain some results related to the vanishing, finiteness, and surjectivity of analytic cohomology groups with multiplier ideal sheaves.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/714","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48252597","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}
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety: the regular functions and the continuous rational functions.
研究了实代数变量:正则函数和连续有理函数上不同函数环的积分闭包的代数和几何性质。
{"title":"Integral closures in real algebraic geometry","authors":"J. Monnier, G. Fichou, Ronan Quarez","doi":"10.1090/jag/769","DOIUrl":"https://doi.org/10.1090/jag/769","url":null,"abstract":"We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety: the regular functions and the continuous rational functions.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45028343","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}
We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible components of these moduli spaces. Our results confirm Geometric Manin’s Conjecture in these examples and show the enumerativity of certain Gromov-Witten invariants.
{"title":"Rational curves on prime Fano threefolds of index 1","authors":"Brian Lehmann, Sho Tanimoto","doi":"10.1090/jag/751","DOIUrl":"https://doi.org/10.1090/jag/751","url":null,"abstract":"We study the moduli spaces of rational curves on prime Fano threefolds of index 1. For general threefolds of most genera we compute the dimension and the number of irreducible components of these moduli spaces. Our results confirm Geometric Manin’s Conjecture in these examples and show the enumerativity of certain Gromov-Witten invariants.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/751","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46708893","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}
We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We also present a numerical criterion for the absence of walls in terms of a discriminant function. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin, and the first author. For the proof we strengthen several known results on Bridgeland stability conditions of abelian threefolds. We show that certain previously constructed stability conditions satisfy the full support property. In particular, the stability manifold is non-empty. We also prove the existence of a Gieseker chamber and determine all wall-crossing contributions. A definition of reduced generalized Donaldson–Thomas invariants for arbitrary Calabi–Yau threefolds with abelian actions is given.
{"title":"Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions","authors":"G. Oberdieck, D. Piyaratne, Yukinobu Toda","doi":"10.1090/JAG/788","DOIUrl":"https://doi.org/10.1090/JAG/788","url":null,"abstract":"We study the reduced Donaldson–Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson–Thomas invariants under all derived autoequivalences, up to explicitly given wall-crossing terms. We also present a numerical criterion for the absence of walls in terms of a discriminant function. For principally polarized abelian threefolds of Picard rank one, the wall-crossing contributions are discussed in detail. The discussion yields evidence for a conjectural formula for curve counting invariants by Bryan, Pandharipande, Yin, and the first author.\u0000\u0000For the proof we strengthen several known results on Bridgeland stability conditions of abelian threefolds. We show that certain previously constructed stability conditions satisfy the full support property. In particular, the stability manifold is non-empty. We also prove the existence of a Gieseker chamber and determine all wall-crossing contributions. A definition of reduced generalized Donaldson–Thomas invariants for arbitrary Calabi–Yau threefolds with abelian actions is given.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46311841","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}
Let XX be a smooth rigid analytic space. We prove that the category of co-admissible wideparen {mathcal {D}_X}-modules supported on a closed smooth subvariety YY of XX is naturally equivalent to the category of co-admissible wideparen {mathcal {D}_Y}-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible wideparen {mathcal {D}_X}-modules.
{"title":"wideparen{𝒟}-modules on rigid analytic spaces II: Kashiwara’s equivalence","authors":"K. Ardakov, S. Wadsley","doi":"10.1090/JAG/709","DOIUrl":"https://doi.org/10.1090/JAG/709","url":null,"abstract":"<p>Let <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> be a smooth rigid analytic space. We prove that the category of co-admissible <inline-formula content-type=\"math/tex\">\u0000<tex-math>\u0000wideparen {mathcal {D}_X}</tex-math></inline-formula>-modules supported on a closed smooth subvariety <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\u0000 <mml:semantics>\u0000 <mml:mi>Y</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <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 naturally equivalent to the category of co-admissible <inline-formula content-type=\"math/tex\">\u0000<tex-math>\u0000wideparen {mathcal {D}_Y}</tex-math></inline-formula>-modules and use this result to construct a large family of pairwise non-isomorphic simple co-admissible <inline-formula content-type=\"math/tex\">\u0000<tex-math>\u0000wideparen {mathcal {D}_X}</tex-math></inline-formula>-modules.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/709","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45772115","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}
We extend the derived algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic K 0 K^0 analogously to the Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.
{"title":"Bivariant derived algebraic cobordism","authors":"Toni Annala","doi":"10.1090/jag/754","DOIUrl":"https://doi.org/10.1090/jag/754","url":null,"abstract":"We extend the derived algebraic bordism of Lowrey and Schürg to a bivariant theory in the sense of Fulton and MacPherson and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings of singular quasi-projective schemes. The extended cobordism is shown to specialize to algebraic \u0000\u0000 \u0000 \u0000 K\u0000 0\u0000 \u0000 K^0\u0000 \u0000\u0000 analogously to the Conner-Floyd theorem in topology. We also give a candidate for the correct definition of Chow rings of singular schemes.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49028393","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}
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