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Nakano positivity of singular Hermitian metrics and vanishing theorems n of Demailly–Nadel–Nakano type 奇异Hermitian度量的Nakano正性与Demaily–Nadel–Nakano型的消失定理
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-04-13 DOI: 10.14231/AG-2022-003
Takahiro Inayama
{"title":"Nakano positivity of singular Hermitian metrics and vanishing theorems n of Demailly–Nadel–Nakano type","authors":"Takahiro Inayama","doi":"10.14231/AG-2022-003","DOIUrl":"https://doi.org/10.14231/AG-2022-003","url":null,"abstract":"In this article, we propose a general definition of Nakano semi-positivity of singular Hermitian metrics on holomorphic vector bundles. By using this positivity notion, we establish $L^2$-estimates for holomorphic vector bundles with Nakano positive singular Hermitian metrics. We also show vanishing theorems, which generalize both Nakano type and Demailly-Nadel type vanishing theorems.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49424525","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}
引用次数: 18
New rational cubic fourfolds arising from Cremona transformations 由克雷莫纳变换引起的新的有理三次四重变换
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-02-29 DOI: 10.14231/ag-2023-014
Yu-Wei Fan, Kuan-Wen Lai
{"title":"New rational cubic fourfolds arising from Cremona transformations","authors":"Yu-Wei Fan, Kuan-Wen Lai","doi":"10.14231/ag-2023-014","DOIUrl":"https://doi.org/10.14231/ag-2023-014","url":null,"abstract":"Are Fourier--Mukai equivalent cubic fourfolds birationally equivalent? We obtain an affirmative answer to this question for very general cubic fourfolds of discriminant 20, where we produce birational maps via the Cremona transformation defined by the Veronese surface. Moreover, by studying how these maps act on the cubics known to be rational, we found new rational examples.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48147063","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}
引用次数: 3
Cancellation theorems for reciprocity sheaves 互易滑轮的消去定理
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-01-22 DOI: 10.14231/ag-2023-005
Alberto Merici, S. Saito
{"title":"Cancellation theorems for reciprocity sheaves","authors":"Alberto Merici, S. Saito","doi":"10.14231/ag-2023-005","DOIUrl":"https://doi.org/10.14231/ag-2023-005","url":null,"abstract":"We prove cancellation theorems for reciprocity sheaves and cube-invariant modulus sheaves with transfers of Kahn--Saito--Yamazaki, generalizing Voevodsky's cancellation theorem for $mathbf{A}^1$-invariant sheaves with transfers. As an application, we get some new formulas for internal hom's of the sheaves $Omega^i$ of absolute K\"ahler differentials.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45921610","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}
引用次数: 6
Motivic integration on the Hitchin fibration 希钦氏纤维的动力整合
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-12-25 DOI: 10.14231/ag-2021-004
F. Loeser, Dimitri Wyss
{"title":"Motivic integration on the Hitchin fibration","authors":"F. Loeser, Dimitri Wyss","doi":"10.14231/ag-2021-004","DOIUrl":"https://doi.org/10.14231/ag-2021-004","url":null,"abstract":"We prove that the moduli spaces of twisted $mathrm{SL}_n$ and $mathrm{PGL}_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow motives. On the level of Hodge numbers this was conjectured by Hausel and Thaddeus, and recently proven by Groechenig, Ziegler and the second author. To adapt their argument, which relies on p-adic integration, we use a version of motivic integration with values in rational Chow motives and the geometry of Neron models to evaluate such integrals on Hitchin fibers.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42418411","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}
引用次数: 8
Modular sheaves on hyperkähler varieties hyperkähler品种的模块化滑轮
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-12-05 DOI: 10.14231/ag-2022-001
K. O’Grady
{"title":"Modular sheaves on hyperkähler varieties","authors":"K. O’Grady","doi":"10.14231/ag-2022-001","DOIUrl":"https://doi.org/10.14231/ag-2022-001","url":null,"abstract":"A torsion free sheaf on a hyperkahler variety $X$ is modular if the discriminant satisfies a certain condition, for example if it is a multiple of $c_2(X)$ the sheaf is modular. The definition is taylor made for torsion-free sheaves on a polarized hyperkahler variety (X,h) which deform to all small deformations of (X,h). For hyperkahlers deformation equivalent to $K3^{[2]}$ we prove an existence and uniqueness result for slope-stable modular vector bundles with certain ranks, $c_1$ and $c_2$. As a consequence we get uniqueness up to isomorphism of the tautological quotient rank $4$ vector bundles on the variety of lines on a generic cubic $4$-dimensional hypersurface, and on the Debarre-Voisin variety associated to a generic skew-symmetric $3$-form on a $10$-dimensional complex vector space. The last result implies that the period map from the moduli space of Debarre-Voisin varieties to the relevant period space is birational.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43655483","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}
引用次数: 8
Bivariant algebraic cobordism with bundles 具有丛的双变代数同基
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-11-28 DOI: 10.14231/ag-2023-015
Toni Annala, Shoji Yokura
{"title":"Bivariant algebraic cobordism with bundles","authors":"Toni Annala, Shoji Yokura","doi":"10.14231/ag-2023-015","DOIUrl":"https://doi.org/10.14231/ag-2023-015","url":null,"abstract":"The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism where the cycles carry a vector bundle on the source as additional data. We show that, over a field of characteristic 0, this extends the analogous homological theory of Lee and Pandharipande constructed earlier. We then proceed to study in detail the restricted theory where only rank 1 vector bundles are allowed, and prove a weak version of projective bundle formula for bivariant cobordism. Since the proof of this theorem works very generally, we introduce precobordism theories over arbitrary Noetherian rings of finite Krull dimension as a reasonable class of theories where the proof can be carried out, and prove some of their basic properties. These results can be considered as the first steps towards a Levine-Morel style algebraic cobordism over a base ring that is not a field of characteristic 0.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47135370","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}
引用次数: 5
A functorial approach to regular homomorphisms 正则同态的一种函数方法
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-11-22 DOI: 10.14231/ag-2023-003
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
{"title":"A functorial approach to regular homomorphisms","authors":"Jeff Achter, Sebastian Casalaina-Martin, Charles Vial","doi":"10.14231/ag-2023-003","DOIUrl":"https://doi.org/10.14231/ag-2023-003","url":null,"abstract":"Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families of algebraically trivial cycles to abelian varieties and thereby define regular homomorphisms in the relative setting, e.g., families of schemes parameterized by a smooth variety over a given field. In that general setting, we establish the existence of an initial regular homomorphism, going by the name of algebraic representative, for codimension-2 cycles on a smooth proper scheme over the base. This extends a result of Murre for codimension-2 cycles on a smooth projective scheme over an algebraically closed field. In addition, we prove base change results for algebraic representatives as well as descent properties for algebraic representatives along separable field extensions. In the case where the base is a smooth variety over a subfield of the complex numbers we identify the algebraic representative for relative codimension-2 cycles with a subtorus of the intermediate Jacobian fibration which was constructed in previous work. \u0000At the heart of our descent arguments is a base change result along separable field extensions for Albanese torsors of separated, geometrically integral schemes of finite type over a field.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46252869","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}
引用次数: 9
On a question of Swann (with an appendix by K?stutis ?esnavi?ius) 关于斯旺的一个问题(附K?stutis esnavi ?国际单位)
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-11-01 DOI: 10.14231/ag-2019-030
D. Popescu
{"title":"On a question of Swann (with an appendix by K?stutis ?esnavi?ius)","authors":"D. Popescu","doi":"10.14231/ag-2019-030","DOIUrl":"https://doi.org/10.14231/ag-2019-030","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41949752","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}
引用次数: 1
$mathbb{P}$-functor versions of the Nakajima operators $mathbb｛P｝$-Nakajima运算符的函子版本
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-11-01 DOI: 10.14231/ag-2019-029
Andreas Krug
{"title":"$mathbb{P}$-functor versions of the Nakajima operators","authors":"Andreas Krug","doi":"10.14231/ag-2019-029","DOIUrl":"https://doi.org/10.14231/ag-2019-029","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48843520","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}
引用次数: 2
Punctual Hilbert schemes for Kleinian singularities as quiver varieties 作为颤动变体的Kleinian奇点的标点Hilbert格式
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-10-29 DOI: 10.14231/ag-2021-021
Alastair Craw, Søren Gammelgaard, 'Ad'am Gyenge, Bal'azs SzendrHoi
{"title":"Punctual Hilbert schemes for Kleinian singularities as quiver varieties","authors":"Alastair Craw, Søren Gammelgaard, 'Ad'am Gyenge, Bal'azs SzendrHoi","doi":"10.14231/ag-2021-021","DOIUrl":"https://doi.org/10.14231/ag-2021-021","url":null,"abstract":"For a finite subgroup $Gammasubset mathrm{SL}(2,mathbb{C})$ and $ngeq 1$, we construct the (reduced scheme underlying the) Hilbert scheme of $n$ points on the Kleinian singularity $mathbb{C}^2/Gamma$ as a Nakajima quiver variety for the framed McKay quiver of $Gamma$, taken at a specific non-generic stability parameter. We deduce that this Hilbert scheme is irreducible (a result previously due to Zheng), normal, and admits a unique symplectic resolution. More generally, we introduce a class of algebras obtained from the preprojective algebra of the framed McKay quiver by a process called cornering, and we show that fine moduli spaces of cyclic modules over these new algebras are isomorphic to quiver varieties for the framed McKay quiver and certain non-generic choices of stability parameter.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45842032","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}
引用次数: 10
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