The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry

被引：36

作者：

Gathmann, Andreas ^{[1
]}

Markwig, Hannah ^{[1
]}

机构：

[1] Univ Kaiserslautern, Dept Math, D-67653 Kaiserslautern, Germany

来源：

MATHEMATISCHE ANNALEN | 2007年 / 338卷 / 04期

关键词：

Primary 14N35; 52B20; Secondary 14N10; 51M20;

D O I：

10.1007/s00208-007-0092-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Some years ago Caporaso and Harris have found a niceway to compute the numbers N(d, g) of complex plane curves of degree d and genus g through 3d + g-1 general points with the help of relative Gromov-Witten invariants. Recently, Mikhalkin has found a way to reinterpret the numbers N(d, g) in terms of tropical geometry and to compute them by counting certain lattice paths in integral polytopes. We relate these two results by defining an analogue of the relative Gromov-Witten invariants and rederiving the Caporaso-Harris formula in terms of both tropical geometry and lattice paths.

引用

页码：845 / 868

页数：24