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Automorphism groups of cubic fourfolds and K3 categories 三次四重和K3范畴的自同构群
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-09-24 DOI: 10.14231/ag-2021-003
Genki Ouchi
{"title":"Automorphism groups of cubic fourfolds and K3 categories","authors":"Genki Ouchi","doi":"10.14231/ag-2021-003","DOIUrl":"https://doi.org/10.14231/ag-2021-003","url":null,"abstract":"In this paper, we study relations between automorphism groups of cubic fourfolds and Kuznetsov components. Firstly, we characterize automorphism groups of cubic fourfolds as subgroups of autoequivalence groups of Kuznetsov components using Bridgeland stability conditions. Secondly, we compare automorphism groups of cubic fourfolds with automorphism groups of their associated K3 surfaces. Thirdly, we note that the existence of a non-trivial symplectic automorphism on a cubic fourfold is related to the existence of associated K3 surfaces.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44006586","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: 7
Hecke correspondences for Hilbert schemes of reducible locally planar curves 可约局部平面曲线Hilbert格式的Hecke对应
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-09-01 DOI: 10.14231/ag-2019-024
Oscar Kivinen
{"title":"Hecke correspondences for Hilbert schemes of reducible locally planar curves","authors":"Oscar Kivinen","doi":"10.14231/ag-2019-024","DOIUrl":"https://doi.org/10.14231/ag-2019-024","url":null,"abstract":"Let C be a complex, reduced, locally planar curve. We extend the results of Rennemo [R14] to reducible curves by constructing an algebra A acting on V = ⊕ n>0H BM ∗ (C [n],Q), where C [n] is the Hilbert scheme of n points on C. If m is the number of irreducible components of C, we realize A as a subalgebra of the Weyl algebra of A2m. We also compute the representation V in the simplest reducible example of a node.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41894768","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
MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3${}^{[n]}$ type K3${}^{[n]}$型低维超kähler流形上的MBM类和收缩轨迹
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-07-30 DOI: 10.14231/ag-2022-008
E. Amerik, M. Verbitsky
{"title":"MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3${}^{[n]}$ type","authors":"E. Amerik, M. Verbitsky","doi":"10.14231/ag-2022-008","DOIUrl":"https://doi.org/10.14231/ag-2022-008","url":null,"abstract":"An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold of K3-type of low dimension using a deformation to a Hilbert scheme of a non-algebraic K3 surface.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49398062","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
Non-Ulrich representation type 非ulrich表示类型
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-07-04 DOI: 10.14231/AG-2021-012
Daniele Faenzi, F. Malaspina, Giangiacomo Sanna
{"title":"Non-Ulrich representation type","authors":"Daniele Faenzi, F. Malaspina, Giangiacomo Sanna","doi":"10.14231/AG-2021-012","DOIUrl":"https://doi.org/10.14231/AG-2021-012","url":null,"abstract":"We show that a smooth projective non-degenerate arithmetically Cohen-Macaulay subvariety X of P^N infinite Cohen-Macaulay type becomes of finite Cohen-Macaulay type by removing Ulrich bundles if and only if N = 5 and X is a quartic scroll or the Segre product of a line and a plane. In turn, we give a complete and explicit classification of ACM bundles over these varieties.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42231540","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
Derived invariants from topological Hochschild homology 拓扑Hochschild同调的导出不变量
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-06-28 DOI: 10.14231/ag-2022-011
Benjamin Antieau, Daniel Bragg
{"title":"Derived invariants from topological Hochschild homology","authors":"Benjamin Antieau, Daniel Bragg","doi":"10.14231/ag-2022-011","DOIUrl":"https://doi.org/10.14231/ag-2022-011","url":null,"abstract":"We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various $p$-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers. As a consequence, we obtain restrictions on the Hodge numbers of derived equivalent varieties, partially extending results of Popa-Schell to positive characteristic.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45537518","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: 7
Curve counting in genus one: Elliptic singularities and relative geometry 一属曲线计数:椭圆奇点和相对几何
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-06-28 DOI: 10.14231/AG-2021-020
L. Battistella, Navid Nabijou, Dhruv Ranganathan
{"title":"Curve counting in genus one: Elliptic singularities and relative geometry","authors":"L. Battistella, Navid Nabijou, Dhruv Ranganathan","doi":"10.14231/AG-2021-020","DOIUrl":"https://doi.org/10.14231/AG-2021-020","url":null,"abstract":"We construct and study the reduced, relative, genus one Gromov-Witten theory of very ample pairs. These invariants form the principal component contribution to relative Gromov-Witten theory in genus one and are relative versions of Zinger's reduced Gromov-Witten invariants. We relate the relative and absolute theories by degeneration of the tangency conditions, and the resulting formulas generalise a well-known recursive calculation scheme put forward by Gathmann in genus zero. The geometric input is a desingularisation of the principal component of the moduli space of genus one logarithmic stable maps to a very ample pair, using the geometry of elliptic singularities. Our study passes through general techniques for calculating integrals on logarithmic blowups of moduli spaces of stable maps, which may be of independent interest.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48605490","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
Small projective spaces and Stillman uniformity for sheaves 小投影空间和斯蒂尔曼均匀的轮轴
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-06-26 DOI: 10.14231/AG-2021-010
D. Erman, Steven V. Sam, A. Snowden
{"title":"Small projective spaces and Stillman uniformity for sheaves","authors":"D. Erman, Steven V. Sam, A. Snowden","doi":"10.14231/AG-2021-010","DOIUrl":"https://doi.org/10.14231/AG-2021-010","url":null,"abstract":"We prove an analogue of Ananyan--Hochster's small subalgebra theorem in the context of sheaves on projective space, and deduce from this a version of Stillman's Conjecture for cohomology tables of sheaves. The main tools in the proof are Draisma's GL-noetherianity theorem and the BGG correspondence.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48131932","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
Deformation of rational singularities and Hodge structure 理性奇点变形与霍奇结构
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-06-10 DOI: 10.14231/ag-2022-014
M. Kerr, R. Laza, M. Saito
{"title":"Deformation of rational singularities and Hodge structure","authors":"M. Kerr, R. Laza, M. Saito","doi":"10.14231/ag-2022-014","DOIUrl":"https://doi.org/10.14231/ag-2022-014","url":null,"abstract":"For a one-parameter degeneration of reduced compact complex analytic spaces of dimension n , we prove the invariance of the frontier Hodge numbers h p,q (that is, those with pq ( n − p )( n − q ) = 0) for the intersection cohomology of the fibers and also for the cohomology of their desingularizations, assuming that the central fiber is reduced, projective, and has only rational singularities. This can be shown to be equivalent to the invariance of the dimension of the cohomology of the structure sheaf since we can prove the Hodge symmetry for all the Hodge numbers h p,q together with E 1 -degeneration of the Hodge-to-de Rham spectral sequence for nearby fibers, assuming only the projectivity of the central fiber. For the proof of the main theorem, we calculate the graded pieces of the induced V -filtration for the first non-zero member of the Hodge filtration on the intersection complex Hodge module of the total space, which coincides with the direct image of the dualizing sheaf of a desingularization. This calculation also implies that the order of nilpotence of the local monodromy is smaller than in the general singularity case by 2 in the situation of the main theorem assuming further smoothness of general fibers.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43629632","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: 11
Genus-one mirror symmetry in the Landau�Ginzburg model 朗道中的属一镜像对称�Ginzburg模型
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-05-01 DOI: 10.14231/AG-2019-013
Dustin Ross
{"title":"Genus-one mirror symmetry in the Landau�Ginzburg model","authors":"Dustin Ross","doi":"10.14231/AG-2019-013","DOIUrl":"https://doi.org/10.14231/AG-2019-013","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47315725","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
The eventual paracanonical map of a variety of maximal Albanese dimension 一类极大Albanese维数的最终准正则映射
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2019-05-01 DOI: 10.14231/AG-2019-014
G. Farkas
{"title":"The eventual paracanonical map of a variety of maximal Albanese dimension","authors":"G. Farkas","doi":"10.14231/AG-2019-014","DOIUrl":"https://doi.org/10.14231/AG-2019-014","url":null,"abstract":"Let $X$ be a smooth complex projective variety such that the Albanese map of $X$ is generically finite onto its image. Here we study the so-called eventual $m$-paracanonical map of $X$ (when $m=1$ we also assume $chi(K_X)>0$). We show that for $m=1$ this map behaves in a similar way to the canonical map of a surface of general type, while it is birational for $m>1$. We also describe it explicitly in several examples.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45324427","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
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