Hodge integrals and Hurwitz numbers via virtual localization

被引：47

作者：

Graber, T ^{[1
]}

Vakil, R

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

来源：

COMPOSITIO MATHEMATICA | 2003年 / 135卷 / 01期

基金：

美国国家科学基金会;

关键词：

Hodge integrals; Hurwitz numbers; virtual localization;

D O I：

10.1023/A:1021791611677

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give another proof of Ekedahl, Lando, Shapiro, and Vainshtein's remarkable formula expressing Hurwitz numbers (counting covers of P-1 with specified simple branch points, and specified branching over one other point) in terms of Hodge integrals. Our proof uses virtual localization on the moduli space of stable maps. We describe how the proof could be simplified by the proper algebro-geometric definition of a 'relative space'. Such a space has recently been defined by J. Li.

引用

页码：25 / 36

页数：12

共 25 条

[1] Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges [J].