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Moduli of elliptic $K3$ surfaces: Monodromy and Shimada root lattice strata n (with an appendix by Markus Kirschmer) 椭圆$K3$曲面的模：Monodromy和Shimada根格层（附Markus Kirschmer附录）
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-01-29 DOI: 10.14231/ag-2022-006
K. Hulek, M. Lonne
{"title":"Moduli of elliptic $K3$ surfaces: Monodromy and Shimada root lattice strata n (with an appendix by Markus Kirschmer)","authors":"K. Hulek, M. Lonne","doi":"10.14231/ag-2022-006","DOIUrl":"https://doi.org/10.14231/ag-2022-006","url":null,"abstract":"In this paper we investigate two stratifications of the moduli space of elliptically fibred K3 surfaces. The first comes from Shimada’s classification of connected components of the moduli of elliptically fibred K3 surfaces and is closely related to the root lattices of the fibration. The second is the monodromy stratification defined by Bogomolov, Petrov and Tschinkel. The main result of the paper is a classification of all positive-dimensional ambi-typical strata, that is, strata which are both Shimada root strata and monodromy strata. We also discuss the relationship with moduli spaces of lattice-polarised K3 surfaces. The appendix by M. Kirschmer contains computational results about the 1-dimensional ambi-typical strata.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41440042","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
Inversion of adjunction for quotient singularities 商奇点的附加反转
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-11-14 DOI: 10.14231/ag-2022-007
Yusuke Nakamura, K. Shibata
{"title":"Inversion of adjunction for quotient singularities","authors":"Yusuke Nakamura, K. Shibata","doi":"10.14231/ag-2022-007","DOIUrl":"https://doi.org/10.14231/ag-2022-007","url":null,"abstract":"We prove the precise inversion of adjunction formula for quotient singularities and klt Cartier divisors. As an application, we prove the semi-continuity of minimal log discrepancies for klt hyperquotient singularities.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48607912","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
Basepoint-freeness thresholds and higher syzygies of abelian threefolds 基点自由阈值和阿贝尔三倍的高协同性
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-08-24 DOI: 10.14231/ag-2022-023
Atsushi Ito
{"title":"Basepoint-freeness thresholds and higher syzygies of abelian threefolds","authors":"Atsushi Ito","doi":"10.14231/ag-2022-023","DOIUrl":"https://doi.org/10.14231/ag-2022-023","url":null,"abstract":"For a polarized abelian variety, Z. Jiang and G. Pareschi introduce an invariant and show that the polarization is basepoint free or projectively normal if the invariant is small. Their result is generalized to higher syzygies by F. Caucci, that is, the polarization satisfies property $(N_p)$ if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we affirmatively answer a question about $(N_p)$ on abelian varieties asked by the author and V. Lozovanu in the three dimensional case.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49001987","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
Canonical models of toric hypersurfaces 环面超曲面的正则模型
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-08-13 DOI: 10.14231/ag-2023-013
V. Batyrev
{"title":"Canonical models of toric hypersurfaces","authors":"V. Batyrev","doi":"10.14231/ag-2023-013","DOIUrl":"https://doi.org/10.14231/ag-2023-013","url":null,"abstract":"Let $Z subset mathbb{T}_d$ be a non-degenerate hypersurface in $d$-dimensional torus $mathbb{T}_d cong (mathbb{C}^*)^d$ defined by a Laurent polynomial $f$ with a given $d$-dimensional Newton polytope $P$. It follows from a theorem of Ishii that $Z$ is birational to a smooth projective variety $X$ of Kodaira dimension $kappa geq 0$ if and only if the Fine interior $F(P)$ of $P$ is nonempty. We define a unique projective model $widetilde{Z}$ of $Z$ having at worst canonical singularities which allows us to obtain minimal models $widehat{Z}$ of $Z$ by crepant morphisms $widehat{Z} to widetilde{Z}$. Moreover, we show that $kappa = min { d-1, dim F(P) }$ and that general fibers in the Iitaka fibration of the canonical model $widetilde{Z}$ are non-degenerate $(d-1-kappa)$-dimensional toric hypersurfaces of Kodaira dimension $0$. Using the rational polytope $F(P)$, we compute the stringy $E$-function of minimal models $widehat{Z}$ and obtain a combinatorial formula for their stringy Euler numbers.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44633498","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
Corrigendum: Integral cohomology of the generalized Kummer fourfold (Algebraic Geometry 5, no. 5 (2018), 523�567) 勘误表：广义Kummer四重的积分上同调（代数几何5，no.5（2018），523�567）
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-07-01 DOI: 10.14231/ag-2020-014
Gr'egoire Menet
{"title":"Corrigendum: Integral cohomology of the generalized Kummer fourfold (Algebraic Geometry 5, no. 5 (2018), 523�567)","authors":"Gr'egoire Menet","doi":"10.14231/ag-2020-014","DOIUrl":"https://doi.org/10.14231/ag-2020-014","url":null,"abstract":"","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46885133","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
Moret-Bailly families and non-liftable schemes 莫雷-贝利家族和不可解除的计划
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-06-30 DOI: 10.14231/ag-2022-004
D. Roessler, Stefan Schroer
{"title":"Moret-Bailly families and non-liftable schemes","authors":"D. Roessler, Stefan Schroer","doi":"10.14231/ag-2022-004","DOIUrl":"https://doi.org/10.14231/ag-2022-004","url":null,"abstract":"Generalizing the Moret-Bailly pencil of supersingular abelian surfaces to higher dimensions, we construct for each field of characteristic p>0 a smooth projective variety with trivial dualizing sheaf that does not formally lift to characteristic zero. Our approach heavily relies on local unipotent group schemes, the Beauville--Bogomolov Decomposition for Kahler manifolds with $c_1=0$, and equivariant deformation theory","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44552043","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
Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces 辛曲面的等变范畴与Bridgeland模空间的固定轨迹
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-06-24 DOI: 10.14231/ag-2022-012
T. Beckmann, G. Oberdieck
{"title":"Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces","authors":"T. Beckmann, G. Oberdieck","doi":"10.14231/ag-2022-012","DOIUrl":"https://doi.org/10.14231/ag-2022-012","url":null,"abstract":"Given an action of a finite group $G$ on the derived category of a smooth projective variety $X$ we relate the fixed loci of the induced $G$-action on moduli spaces of stable objects in $D^b(mathrm{Coh}(X))$ with moduli spaces of stable objects in the equivariant category $D^b(mathrm{Coh}(X))_G$. As an application we obtain a criterion for the equivariant category of a symplectic action on the derived category of a symplectic surface to be equivalent to the derived category of a surface. This generalizes the derived McKay correspondence, and yields a general framework for describing fixed loci of symplectic group actions on moduli spaces of stable objects on symplectic surfaces.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47773935","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
Mather classes and conormal spaces of Schubert varieties in cominuscule spaces 组合空间中舒伯特变种的Mather类与共形空间
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-06-08 DOI: 10.14231/ag-2023-019
L. Mihalcea, R. Singh
{"title":"Mather classes and conormal spaces of Schubert varieties in cominuscule spaces","authors":"L. Mihalcea, R. Singh","doi":"10.14231/ag-2023-019","DOIUrl":"https://doi.org/10.14231/ag-2023-019","url":null,"abstract":"Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q to G/P$. We apply this to find formulae for the local Euler obstructions of Schubert varieties, and for the torus equivariant localizations of the conormal spaces of these Schubert varieties. We conjecture positivity properties for the local Euler obstructions and for the Schubert expansion of Mather classes. We check the conjectures in many cases, by utilizing results of Boe and Fu about the characteristic cycles of the intersection homology sheaves of Schubert varieties. We also conjecture that certain `Mather polynomials' are unimodal in general Lie type, and log concave in type A.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41949523","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
On the boundedness of $n$-folds with $kappa(X)=n-1$ 关于具有 $kappa(X)=n-1$ 的 $n$ 折叠的有界性
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-05-12 DOI: 10.14231/AG-2024-011
Stefano Filipazzi
{"title":"On the boundedness of $n$-folds with $kappa(X)=n-1$","authors":"Stefano Filipazzi","doi":"10.14231/AG-2024-011","DOIUrl":"https://doi.org/10.14231/AG-2024-011","url":null,"abstract":"In this note we study certain sufficient conditions for a set of minimal klt pairs $(X,Delta)$ with $kappa(X,Delta)=dim(X)-1$ to be bounded.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141205500","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
Cohomological Hall algebra of Higgs sheaves on a curve 曲线上希格斯轴的上同霍尔代数
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2020-05-01 DOI: 10.14231/AG-2020-010
G. Farkas
{"title":"Cohomological Hall algebra of Higgs sheaves on a curve","authors":"G. Farkas","doi":"10.14231/AG-2020-010","DOIUrl":"https://doi.org/10.14231/AG-2020-010","url":null,"abstract":"We define the cohomological Hall algebra ${AHA}_{Higgs(X)}$ of the ($2$-dimensional) Calabi-Yau category of Higgs sheaves on a smooth projective curve $X$, as well as its nilpotent and semistable variants, in the context of an arbitrary oriented Borel-Moore homology theory. In the case of usual Borel-Moore homology, ${AHA}_{Higgs(X)}$ is a module over the (universal) cohomology ring $mathbb{H}$ of the stacks of coherent sheaves on $X$ . We show that it is a torsion-free $mathbb{H}$-module, and we provide an explicit collection of generators (the collection of fundamental classes $[Coh_{r,d}]$ of the zero-sections of the map $Higgs_{r,d} to Coh_{r,d}$, for $r geq 0, d in Z$).","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66815974","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
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