ADE surfaces and their moduli

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2017-12-21 DOI:10.1090/jag/762

V. Alexeev, A. Thompson

引用次数: 12

Abstract

We define a class of surfaces corresponding to the A D E ADE root lattices and construct compactifications of their moduli spaces as quotients of projective varieties for Coxeter fans, generalizing Losev-Manin spaces of curves. We exhibit modular families over these moduli spaces, which extend to families of stable pairs over the compactifications. One simple application is a geometric compactification of the moduli of rational elliptic surfaces that is a finite quotient of a projective toric variety.

查看原文本刊更多论文

ADE曲面及其模

我们定义了一类对应于a DE ADE根格的曲面，并构造了它们的模空间的紧化，作为Coxeter扇形的射影变商，推广了曲线的Losev-Manin空间。我们在这些模空间上展示了模族，并将其推广到紧化上的稳定对族。一个简单的应用是有理椭圆曲面模的几何紧化，它是一个射影环变的有限商。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.