Algebraic Geometry最新文献_第6页

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

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":" ","pages":""},"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

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

引用次数: 1

On the construction of valuations and generating sequences on hypersurface singularities 关于超曲面奇点上赋值的构造与生成序列

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-04-24 DOI: 10.14231/ag-2021-022

S. Cutkosky, H. Mourtada, B. Teissier

{"title":"On the construction of valuations and generating sequences on hypersurface singularities","authors":"S. Cutkosky, H. Mourtada, B. Teissier","doi":"10.14231/ag-2021-022","DOIUrl":"https://doi.org/10.14231/ag-2021-022","url":null,"abstract":"Suppose that (K, $nu$) is a valued field, f (z) $in$ K[z] is a unitary and irreducible polynomial and (L, $omega$) is an extension of valued fields, where L = K[z]/(f (z)). Further suppose that A is a local domain with quotient field K such that $nu$ has nonnegative value on A and positive value on its maximal ideal, and that f (z) is in A[z]. This paper is devoted to the problem of describing the structure of the associated graded ring gr $omega$ A[z]/(f (z)) of A[z]/(f (z)) for the filtration defined by $omega$ as an extension of the associated graded ring of A for the filtration defined by $nu$. In particular we give an algorithm which in many cases produces a finite set of elements of A[z]/(f (z)) whose images in gr $omega$ A[z]/(f (z)) generate it as a gr $nu$ A-algebra as well as the relations between them. We also work out the interactions of our method of computation with phenomena which complicate the study of ramification and local uniformization in positive characteristic , such as the non tameness and the defect of an extension. For valuations of rank one in a separable extension of valued fields (K, $nu$) $subset$ (L, $omega$) as above our algorithm produces a generating sequence in a local birational extension A1 of A dominated by $nu$ if and only if there is no defect. In this case, gr $omega$ A1[z]/(f (z)) is a finitely presented gr $nu$ A1-module.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48819931","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

Finite torsors on projective schemes defined over a discrete valuation ring 离散赋值环上定义的投影方案上的有限扭算子

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-04-24 DOI: 10.14231/ag-2023-001

P. H. Hai, J. Santos

引用次数: 3

Arithmetic occult period maps 算术隐期图

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-04-08 DOI: 10.14231/AG-2020-021

Jeff Achter

引用次数: 3

Logarithmic Gromov–Witten theory with expansions 带展开式的对数Gromov-Witten理论