Monodromy and vanishing cycles in toric surfaces

被引：8
|
作者：
Salter, Nick [1 ]
机构：
[1] Columbia Univ, Dept Math, 2990 Broadway, New York, NY 10027 USA
来源：
INVENTIONES MATHEMATICAE | 2019年 / 216卷 / 01期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00222-018-0845-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an ample line bundle on a toric surface, a question of Donaldson asks which simple closed curves can be vanishing cycles for nodal degenerations of smooth curves in the complete linear system. This paper provides a complete answer. This is accomplished by reformulating the problem in terms of the mapping class group-valued monodromy of the linear system, and giving a precise determination of this monodromy group.
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页码：153 / 213
页数：61
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