Algebraic Geometry最新文献_第7页

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

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-03-21 DOI: 10.14231/ag-2022-022

Dhruv Ranganathan

引用次数: 46

The Clemens–Griffiths method over non-closed fields 非闭合场上的Clemens-Griffiths方法

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-03-19 DOI: 10.14231/AG-2020-025

Olivier Benoist, Olivier Benoist, Olivier Wittenberg, Olivier Wittenberg

引用次数: 21

Dualit� et principe local-global pour les anneaux locaux hens�liens de dimension 2 n (avec un appendice de Jo�l Riou) 二维链接局部环的对偶性和局部-全局原理(附Jo�l Riou附录)

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-03-01 DOI: 10.14231/ag-2019-008

Diego Izquierdo

引用次数: 0

Teissier's problem on the proportionality of big and nef classes over a compact K�hler manifold 紧化K ` hler流形上大类和小类的比例问题

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-03-01 DOI: 10.14231/AG-2019-009

Jian Xiao

引用次数: 4

The Donaldson–Thomas partition function of the banana manifold n (with an appendix coauthored with Stephen Pietromonaco) 香蕉流形n的Donaldson-Thomas配分函数(附与Stephen Pietromonaco合著的附录)

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-02-22 DOI: 10.14231/ag-2021-002

J. Bryan

{"title":"The Donaldson–Thomas partition function of the banana manifold n (with an appendix coauthored with Stephen Pietromonaco)","authors":"J. Bryan","doi":"10.14231/ag-2021-002","DOIUrl":"https://doi.org/10.14231/ag-2021-002","url":null,"abstract":"A banana manifold is a compact Calabi-Yau threefold, fibered by Abelian surfaces, whose singular fibers have a singular locus given by a \"banana configuration of curves\". A basic example is given by $X_{ban}$, the blowup along the diagonal of the fibered product of a generic rational elliptic surface $Sto mathbb{P}^{1}$ with itself. \u0000In this paper we give a closed formula for the Donaldson-Thomas partition function of the banana manifold $X_{ban }$ restricted to the 3-dimensional lattice $Gamma$ of curve classes supported in the fibers of $X_{ban}to mathbb{P}^{1}$. It is given by [ Z_{Gamma}(X_{ban}) = prod_{d_{1},d_{2},d_{3}geq 0} prod_{k} left(1-p^{k}Q_{1}^{d_{1}}Q_{2}^{d_{2}}Q_{3}^{d_{3}}right)^{-12c(||mathbf{d} ||,k)} ] where $||mathbf{d} || = 2d_{1}d_{2}+ 2d_{2}d_{3}+ 2d_{3}d_{1}-d_{1}^{2}-d_{2}^{2}-d_{3}^{2}$, and the coefficients $c(a,k)$ have a generating function given by an explicit ratio of theta functions. This formula has interesting properties and is closely realated to the equivariant elliptic genera of $operatorname{Hilb} (mathbb{C}^{2})$. In an appendix with S. Pietromonaco, it is shown that the corresponding genus $g$ Gromov-Witten potential $F_{g}$ is a genus 2 Siegel modular form of weight $2g-2$ for $ggeq 2$; namely it is the Skoruppa-Maass lift of a multiple of an Eisenstein series: $frac{6|B_{2g}|}{g(2g-2)!} E_{2g}(tau )$.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2019-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41545663","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: 13

Rigid isotopy of maximally writhed links 最大扭链的刚性同位素

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-02-11 DOI: 10.14231/AG-2021-006

G. Mikhalkin, S. Orevkov

引用次数: 2

A filling-in problem and moderate degenerations of minimal algebraic varieties 一个填充问题与极小代数变种的适度退化

IF 1.5 1区数学

Algebraic Geometry Pub Date : 2019-01-01 DOI: 10.14231/AG-2019-002

S. Takayama

引用次数: 2