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The Hrushovski–Lang–Weil estimates 赫鲁晓夫斯基-朗-威尔估计
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-06-20 DOI: 10.14231/ag-2022-020
K. V. Shuddhodan, Y. Varshavsky
{"title":"The Hrushovski–Lang–Weil estimates","authors":"K. V. Shuddhodan, Y. Varshavsky","doi":"10.14231/ag-2022-020","DOIUrl":"https://doi.org/10.14231/ag-2022-020","url":null,"abstract":"In this work we give a geometric proof of Hrushovski’s generalization of the LangWeil estimates on the number of points in the intersection of a correspondence with the graph of Frobenius.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41626041","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
An obstruction to lifting to characteristic 0 提升到特性0的障碍
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-06-15 DOI: 10.14231/ag-2023-011
H. Esnault, V. Srinivas, J. Stix
{"title":"An obstruction to lifting to characteristic 0","authors":"H. Esnault, V. Srinivas, J. Stix","doi":"10.14231/ag-2023-011","DOIUrl":"https://doi.org/10.14231/ag-2023-011","url":null,"abstract":"We introduce a new obstruction to lifting smooth proper varieties in characteristic $p>0$ to characteristic $0$. It is based on Grothendieck's specialization homomorphism and the resulting discrete finiteness properties of 'etale fundamental groups.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48714807","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
Quasi-plurisubharmonic envelopes 2: Bounds on Monge–Ampère volumes 拟多次谐波包络2:蒙日-安培体积上的界
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-06-08 DOI: 10.14231/AG-2022-021
V. Guedj, C. H. Lu
{"title":"Quasi-plurisubharmonic envelopes 2: Bounds on Monge–Ampère volumes","authors":"V. Guedj, C. H. Lu","doi":"10.14231/AG-2022-021","DOIUrl":"https://doi.org/10.14231/AG-2022-021","url":null,"abstract":"In cite{GL21a} we have developed a new approach to $L^{infty}$-a priori estimates for degenerate complex Monge-Amp`ere equations, when the reference form is closed. This simplifying assumption was used to ensure the constancy of the volumes of Monge-Amp`ere measures. We study here the way these volumes stay away from zero and infinity when the reference form is no longer closed. We establish a transcendental version of the Grauert-Riemenschneider conjecture, partially answering conjectures of Demailly-Pu{a}un cite{DP04} and Boucksom-Demailly-Pu{a}un-Peternell cite{BDPP13}. Our approach relies on a fine use of quasi-plurisubharmonic envelopes. The results obtained here will be used in cite{GL21b} for solving degenerate complex Monge-Amp`ere equations on compact Hermitian varieties.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45020220","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
Planes in cubic fourfolds 四层立体平面
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-05-28 DOI: 10.14231/ag-2023-007
A. Degtyarev, I. Itenberg, J. C. Ottem
{"title":"Planes in cubic fourfolds","authors":"A. Degtyarev, I. Itenberg, J. C. Ottem","doi":"10.14231/ag-2023-007","DOIUrl":"https://doi.org/10.14231/ag-2023-007","url":null,"abstract":"We show that the maximal number of planes in a complex smooth cubic fourfold in ${mathbb P}^5$ is $405$, realized by the Fermat cubic only; the maximal number of real planes in a real smooth cubic fourfold is $357$, realized by the so-called Clebsch--Segre cubic. Altogether, there are but three (up to projective equivalence) cubics with more than $350$ planes.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44661053","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
A non-Archimedean analogue of Campana's notion of specialness 坎帕纳的特殊性概念的非阿基米德类比
IF 1.5 1区 数学
Algebraic Geometry Pub Date : 2021-05-10 DOI: 10.14231/ag-2023-009
J. Morrow, Giovanni Rosso
{"title":"A non-Archimedean analogue of Campana's notion of specialness","authors":"J. Morrow, Giovanni Rosso","doi":"10.14231/ag-2023-009","DOIUrl":"https://doi.org/10.14231/ag-2023-009","url":null,"abstract":"Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let $mathscr{X}$ be a $K$-analytic space (in the sense of Huber). In this work, we pursue a non-Archimedean characterization of Campana's notion of specialness. We say $mathscr{X}$ is $K$-analytically special if there exists a connected, finite type algebraic group $G/K$, a dense open subset $mathscr{U}subset G^{text{an}}$ with $text{codim}(G^{text{an}}setminus mathscr{U}) geq 2$, and an analytic morphism $mathscr{U} to mathscr{X}$ which is Zariski dense. With this definition, we prove several results which illustrate that this definition correctly captures Campana's notion of specialness in the non-Archimedean setting. These results inspire us to make non-Archimedean counterparts to conjectures of Campana. As preparation for our proofs, we prove auxiliary results concerning the indeterminacy locus of a meromorphic mapping between $K$-analytic spaces, the notion of pseudo-$K$-analytically Brody hyperbolic, and extensions of meromorphic maps from smooth, irreducible $K$-analytic spaces to the analytification of a semi-abelian variety.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2021-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46751585","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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