Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic hyperbolicity of very general surfaces in toric threefolds.
{"title":"Algebraic hyperbolicity for surfaces in toric threefolds","authors":"Christian Haase, N. Ilten","doi":"10.1090/JAG/770","DOIUrl":"https://doi.org/10.1090/JAG/770","url":null,"abstract":"Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic hyperbolicity of very general surfaces in toric threefolds.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42274765","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 use the Borisov-Keum equations of a fake projective plane and the Borisov-Yeung equations of the Cartwright-Steger surface to show the existence of a regular surface with canonical map of degree 36 and of an irregular surface with canonical map of degree 27. As a by-product, we get equations (over a finite field) for the Z / 3 mathbb {Z}/3 -invariant fibres of the Albanese fibration of the Cartwright-Steger surface and show that they are smooth.
{"title":"Surfaces with canonical map of maximum degree","authors":"Carlos Rito","doi":"10.1090/JAG/761","DOIUrl":"https://doi.org/10.1090/JAG/761","url":null,"abstract":"We use the Borisov-Keum equations of a fake projective plane and the Borisov-Yeung equations of the Cartwright-Steger surface to show the existence of a regular surface with canonical map of degree 36 and of an irregular surface with canonical map of degree 27. As a by-product, we get equations (over a finite field) for the \u0000\u0000 \u0000 \u0000 \u0000 Z\u0000 \u0000 \u0000 /\u0000 \u0000 3\u0000 \u0000 mathbb {Z}/3\u0000 \u0000\u0000-invariant fibres of the Albanese fibration of the Cartwright-Steger surface and show that they are smooth.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2019-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44853823","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 construct a compactification of the moduli space of Drinfeld modules of rank rr and level NN as a moduli space of AA-reciprocal maps. This is closely related to the Satake compactification but not exactly the same. The construction involves some technical assumptions on NN that are satisfied for a cofinal set of ideals NN. In the special case where A=Fq[t]A=mathbb {F}_q[t] and N=(tn)N=(t^n)
{"title":"Compactification of Drinfeld moduli spaces as moduli spaces of 𝐴-reciprocal maps and consequences for Drinfeld modular forms","authors":"R. Pink","doi":"10.1090/jag/772","DOIUrl":"https://doi.org/10.1090/jag/772","url":null,"abstract":"<p>We construct a compactification of the moduli space of Drinfeld modules of rank <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\">\u0000 <mml:semantics>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and level <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> as a moduli space of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A\">\u0000 <mml:semantics>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">A</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-reciprocal maps. This is closely related to the Satake compactification but not exactly the same. The construction involves some technical assumptions on <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that are satisfied for a cofinal set of ideals <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N\">\u0000 <mml:semantics>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">N</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In the special case where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A equals double-struck upper F Subscript q Baseline left-bracket t right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">F</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>q</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">A=mathbb {F}_q[t]</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=\"upper N equals left-parenthesis t Superscript n Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">N=(t^n)</mml:annotation>\u0000 </mml:semanti","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2019-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45193739","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 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":null,"pages":null},"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":null,"pages":null},"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}
We consider μpmu _p- and αpalpha _p-actions on RDP K3 surfaces (K3 surfaces with rational double point (RDP) singularities allowed) in characteristic p>0p > 0. We study possible characteristics, quotient surfaces, and quotient singularities. It turns out that these properties of μpmu _p- and αpalpha _p-actions are analogous to those of Z/lZmathbb {Z}/lmathbb {Z}-actions (for primes l
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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