Decomposition of degenerate Gromov-Witten invariants

被引：35

作者：

Abramovich, Dan ^{[1
]}

Chen, Qile ^{[2
]}

Gross, Mark ^{[3
]}

Siebert, Bernd ^{[4
]}

机构：

[1] Brown Univ, Dept Math, Box 1917, Providence, RI 02912 USA

[2] Boston Coll, Dept Math, Chestnut Hill, MA 02467 USA

[3] Ctr Math Sci, DPMMS, Wilberforce Rd, Cambridge CB3 0WB, England

[4] Univ Texas Austin, Dept Math, 2515 Speedway, Austin, TX 78712 USA

来源：

COMPOSITIO MATHEMATICA | 2020年 / 156卷 / 10期

基金：

英国工程与自然科学研究理事会;

关键词：

logarithmic Gromov-Witten invariant; moduli stack; logarithmic stable map; degeneration; decomposition; tropical curve; tropical map; rigid tropical curve; Artin fan; STABLE LOGARITHMIC MAPS; HOLOMORPHIC-CURVES; GEOMETRY; MODULI; TROPICALIZATION; STACKS; SPACE;

D O I：

10.1112/S0010437X20007393

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a decomposition formula of logarithmic Gromov-Witten invariants in a degeneration setting. A one-parameter log smooth family X -> B with singular fibre over b(0) is an element of B yields a family M(X/B, beta). B of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over b(0) in terms of rigid tropical maps to the tropicalization of X/B. This generalizes one aspect of known results in the case that the fibre Xb(0) is a normal crossings union of two divisors. We exhibit our formulas in explicit examples.

引用

页码：2020 / 2075

页数：56

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