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Smoothing semi-smooth stable Godeaux surfaces 平滑半光滑稳定的Godeaux曲面
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-05-03 DOI: 10.14231/ag-2022-015
B. Fantechi, M. Franciosi, R. Pardini
{"title":"Smoothing semi-smooth stable Godeaux surfaces","authors":"B. Fantechi, M. Franciosi, R. Pardini","doi":"10.14231/ag-2022-015","DOIUrl":"https://doi.org/10.14231/ag-2022-015","url":null,"abstract":"We show that all the semi-smooth stable complex Godeaux surfaces, classified in [FPR18a], are smoothable, and that the moduli stack is smooth of the expected dimension 8 at the corresponding points. 2020 Mathematics Subject Classification: 14J10, 14D15, 14J29.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46303612","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
A cohomological nonabelian Hodge Theorem in positive characteristic 一个具有正特征的上同调非贝利亚Hodge定理
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-04-27 DOI: 10.14231/ag-2022-018
M. A. Cataldo, Siqing Zhang
{"title":"A cohomological nonabelian Hodge Theorem in positive characteristic","authors":"M. A. Cataldo, Siqing Zhang","doi":"10.14231/ag-2022-018","DOIUrl":"https://doi.org/10.14231/ag-2022-018","url":null,"abstract":"We start with a curve over an algebraically closed ground field of positive characteristic p > 0. By using specialization in cohomology techniques, under suitable natural coprimality conditions, we prove a cohomological Simpson Correspondence between the moduli space of Higgs bundles and the one of connections on the curve. We also prove a new p-multiplicative periodicity concerning the cohomology rings of Dolbeault moduli spaces of degrees differing by a factor of p. By coupling this p-periodicity in characteristic p with lifting/specialization techniques in mixed characteristic, we find, in arbitrary characteristic, cohomology ring isomorphisms between the cohomology rings of Dolbeault moduli spaces for different degrees coprime to the rank. It is interesting that this last result is proved as follows: we prove a weaker version in positive characteristic; we lift and strengthen the weaker version to the result in characteristic zero; finally, we specialize the result to positive characteristic. The moduli spaces we work with admit certain natural morphisms (Hitchin, de Rham-Hitchin, Hodge-Hitchin), and all the cohomology ring isomorphisms we find are filtered isomorphisms for the resulting perverse Leray filtrations.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48482020","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
Logarithmic intersections of double ramification cycles 双分支环的对数交集
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-04-23 DOI: 10.14231/ag-2022-017
D. Holmes, Rosa Schwarz
{"title":"Logarithmic intersections of double ramification cycles","authors":"D. Holmes, Rosa Schwarz","doi":"10.14231/ag-2022-017","DOIUrl":"https://doi.org/10.14231/ag-2022-017","url":null,"abstract":"We describe a theory of logarithmic Chow rings and tautological subrings for logarithmically smooth algebraic stacks, via a generalisation of the notion of piecewise-polynomial functions. Using this machinery we prove that the double-double ramification cycle lies in the tautological subring of the (classical) Chow ring of the moduli space of curves, and that the logarithmic double ramification cycle is divisorial (as conjectured by Molcho, Pandharipande, and Schmitt).","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46021901","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: 14
Deformations of rational curves on primitive symplectic varieties and applications 原始辛变量上有理曲线的变形及其应用
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-03-30 DOI: 10.14231/ag-2023-006
C. Lehn, Giovanni Mongardi, Gianluca Pacienza
{"title":"Deformations of rational curves on primitive symplectic varieties and applications","authors":"C. Lehn, Giovanni Mongardi, Gianluca Pacienza","doi":"10.14231/ag-2023-006","DOIUrl":"https://doi.org/10.14231/ag-2023-006","url":null,"abstract":"We study the deformation theory of rational curves on primitive symplectic varieties and show that if the rational curves cover a divisor, then, as in the smooth case, they deform along their Hodge locus in the universal locally trivial deformation. As applications, we extend Markman's deformation invariance of prime exceptional divisors along their Hodge locus to this singular framework and provide existence results for uniruled ample divisors on primitive symplectic varieties which are locally trivial deformations of any moduli space of semistable objects on a projective $K3$ or fibers of the Albanese map of those on an abelian surface. We also present an application to the existence of prime exceptional divisors.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48752402","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
On wormholes in the moduli space of surfaces 曲面模空间中的虫洞
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-02-03 DOI: 10.14231/ag-2022-002
G. Urz'ua, Nicol'as Vilches
{"title":"On wormholes in the moduli space of surfaces","authors":"G. Urz'ua, Nicol'as Vilches","doi":"10.14231/ag-2022-002","DOIUrl":"https://doi.org/10.14231/ag-2022-002","url":null,"abstract":"We study a certain wormholing phenomenon that takes place in the Kollár–Shepherd-Barron–Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs because of the appearance of particular extremal P-resolutions in surfaces on the KBSA boundary. We state a general wormhole conjecture, and we prove it for a wide range of cases. At the end, we discuss some topological properties and open questions.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45153038","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
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":"1 1","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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
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