THE TROPICAL VERTEX

被引：94

作者：

Gross, Mark ^{[1
]}

Pandharipande, Rahul ^{[2
]}

Siebert, Bernd ^{[3
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[3] Univ Hamburg, Dept Math, D-20146 Hamburg, Germany

来源：

DUKE MATHEMATICAL JOURNAL | 2010年 / 153卷 / 02期

基金：

美国国家科学基金会;

关键词：

GROMOV-WITTEN INVARIANTS; CURVES;

D O I：

10.1215/00127094-2010-025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus zero relative Gromov-Witten invariants of toric surfaces. The relative invariants which arise have full tangency to a toric divisor at a single unspecified point. The method uses scattering diagrams, tropical curve counts, degeneration formulas, and exact multiple cover calculations in orbifold Gromov-Witten theory.

引用

页码：297 / 362

页数：66

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