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The Mumford�Tate conjecture for products of abelian varieties 关于阿贝尔变积的Mumford - Tate猜想
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2018-04-18 DOI: 10.14231/ag-2019-028
J. Commelin
{"title":"The Mumford�Tate conjecture for products of abelian varieties","authors":"J. Commelin","doi":"10.14231/ag-2019-028","DOIUrl":"https://doi.org/10.14231/ag-2019-028","url":null,"abstract":"Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K subset mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the $ell$-adic 'etale cohomology groups of~$X$ (namely, a Galois representation) and certain extra structure on the singular cohomology groups of~$X$ (namely, a Hodge structure) convey the same information. \u0000The main result of this paper says that if $A_1$ and~$A_2$ are abelian varieties (or abelian motives) over~$K$, and the Mumford--Tate conjecture holds for both~$A_1$ and~$A_2$, then it holds for $A_1 times A_2$. These results do not depend on the embedding $K subset CC$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44621202","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: 15
Irreducible symplectic varieties from moduli spaces of sheaves on K3 and Abelian surfaces K3和Abelian曲面上束模空间的不可约辛变
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2018-02-04 DOI: 10.14231/ag-2023-012
A. Perego, A. Rapagnetta
{"title":"Irreducible symplectic varieties from moduli spaces of sheaves on K3 and Abelian surfaces","authors":"A. Perego, A. Rapagnetta","doi":"10.14231/ag-2023-012","DOIUrl":"https://doi.org/10.14231/ag-2023-012","url":null,"abstract":"We show that the moduli spaces of sheaves on a projective K3 surface are irreducible symplectic varieties, and that the same holds for the fibers of the Albanese map of moduli spaces of sheaves on an Abelian surface.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2018-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44593338","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: 0
Twisted cubics on cubic fourfolds and stability conditions 立方四重上的扭曲立方及其稳定性条件
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2018-02-04 DOI: 10.14231/ag-2023-022
Chunyi Li, L. Pertusi, Xiaolei Zhao
{"title":"Twisted cubics on cubic fourfolds and stability conditions","authors":"Chunyi Li, L. Pertusi, Xiaolei Zhao","doi":"10.14231/ag-2023-022","DOIUrl":"https://doi.org/10.14231/ag-2023-022","url":null,"abstract":"We give an interpretation of the Fano variety of lines on a cubic fourfold and of the hyperkahler eightfold, constructed by Lehn, Lehn, Sorger and van Straten from twisted cubic curves in a cubic fourfold non containing a plane, as moduli spaces of Bridgeland stable objects in the Kuznetsov component. As a consequence, we reprove the categorical version of Torelli Theorem for cubic fourfolds, we obtain the identification of the period point of LLSvS eightfold with that of the Fano variety, and we discuss derived Torelli Theorem for cubic fourfolds.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2018-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45890540","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: 35
A remark on uniform boundedness for Brauer groups 关于Brauer群一致有界性的一个注记
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2018-01-22 DOI: 10.14231/ag-2020-017
A. Cadoret, Franccois Charles
{"title":"A remark on uniform boundedness for Brauer groups","authors":"A. Cadoret, Franccois Charles","doi":"10.14231/ag-2020-017","DOIUrl":"https://doi.org/10.14231/ag-2020-017","url":null,"abstract":"The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of $ell$-primary torsion in the Brauer group. We show that this finiteness is actually uniform in one-dimensional families for varieties that satisfy the Tate conjecture for divisors -- e.g. abelian varieties and $K3$ surfaces.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2018-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46191817","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: 12
Derived categories and the genus of space curves 导出范畴与空间曲线的亏格
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2018-01-08 DOI: 10.14231/AG-2020-006
Emanuele Macrì, B. Schmidt
{"title":"Derived categories and the genus of space curves","authors":"Emanuele Macrì, B. Schmidt","doi":"10.14231/AG-2020-006","DOIUrl":"https://doi.org/10.14231/AG-2020-006","url":null,"abstract":"We generalize a classical result about the genus of curves in projective space by Gruson and Peskine to principally polarized abelian threefolds of Picard rank one. The proof is based on wall-crossing techniques for ideal sheaves of curves in the derived category. In the process, we obtain bounds for Chern characters of other stable objects such as rank two sheaves. The argument gives a proof for projective space as well. In this case these techniques also indicate an approach for a conjecture by Hartshorne and Hirschowitz and we prove first steps towards it.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2018-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41847176","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: 16
$operatorname{CH}_{0}$-trivialité universelle d'hypersurfaces cubiques presque diagonales $operatorname{CH}_｛0｝$-几乎对角线立方超曲面的普遍琐碎性
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-11-01 DOI: 10.14231/ag-2017-029
Jean-Louis Colliot-Thélène
{"title":"$operatorname{CH}_{0}$-trivialité universelle d'hypersurfaces cubiques presque diagonales","authors":"Jean-Louis Colliot-Thélène","doi":"10.14231/ag-2017-029","DOIUrl":"https://doi.org/10.14231/ag-2017-029","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47056145","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: 0
Properness criteria for families of coherent analytic spaces 相干解析空间族的性质准则
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-10-04 DOI: 10.14231/AG-2020-015
M. Toma
{"title":"Properness criteria for families of coherent analytic spaces","authors":"M. Toma","doi":"10.14231/AG-2020-015","DOIUrl":"https://doi.org/10.14231/AG-2020-015","url":null,"abstract":"We extend Langton's valuative criterion for families of coherent algebraic sheaves to a complex analytic set-up. As a consequence we derive a set of sufficient conditions for the compactness of a moduli space of semistable sheaves over a compact complex manifold. This applies also to some cases appearing in complex projective geometry not covered by previous results.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48270226","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: 4
Segre classes of tautological bundles on Hilbert schemes of surfaces Hilbert曲面方案上的重言丛的Segre类
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-21 DOI: 10.14231/AG-2019-010
C. Voisin
{"title":"Segre classes of tautological bundles on Hilbert schemes of surfaces","authors":"C. Voisin","doi":"10.14231/AG-2019-010","DOIUrl":"https://doi.org/10.14231/AG-2019-010","url":null,"abstract":"We first give an alternative proof, based on a simple geometric argument, of a result of Marian, Oprea and Pandharipande on top Segre classes of the tautological bundles on Hilbert schemes of $K3$ surfaces equipped with a line bundle. We then turn to the blow-up of $K3$ surface at one point and establish vanishing results for the corresponding top Segre classes in a certain range. This determines, at least theoretically, all top Segre classes of tautological bundles for any pair $(Sigma,H),,Hin {rm Pic},Sigma$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43453053","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: 26
Derived category of moduli of pointed curves. I 点曲线模的导出范畴。我
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-21 DOI: 10.14231/AG-2020-026
Ana-Maria Castravet, J. Tevelev
{"title":"Derived category of moduli of pointed curves. I","authors":"Ana-Maria Castravet, J. Tevelev","doi":"10.14231/AG-2020-026","DOIUrl":"https://doi.org/10.14231/AG-2020-026","url":null,"abstract":"This is the first paper in the sequence devoted to derived category of moduli spaces of curves of genus $0$ with marked points. We develop several approaches to describe it equivariantly with respect to the action of the symmetric group permuting marked points. We construct an equivariant full exceptional collection on the Losev-Manin space which categorifies derangements.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43105964","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: 21
On the (non-)vanishing of syzygies of Segre embeddings 关于分段嵌入合子的(非)消失
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2017-08-12 DOI: 10.14231/AG-2019-026
Luke Oeding, Claudiu Raicu, Steven V. Sam
{"title":"On the (non-)vanishing of syzygies of Segre embeddings","authors":"Luke Oeding, Claudiu Raicu, Steven V. Sam","doi":"10.14231/AG-2019-026","DOIUrl":"https://doi.org/10.14231/AG-2019-026","url":null,"abstract":"We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our bounds are tight for Segre embeddings of products of P^1. This generalizes results of Rubei concerning the Green-Lazarsfeld property N_p for Segre embeddings. Our methods combine the Kempf-Weyman geometric technique for computing syzygies, the Ein-Erman-Lazarsfeld approach to proving non-vanishing of Betti numbers, and the theory of algebras with straightening laws.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2017-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44574229","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
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