Monodromy and vanishing cycles in toric surfaces
Algebraic Geometry
2018-12-07 v2 Geometric Topology
Abstract
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.
Cite
@article{arxiv.1710.08042,
title = {Monodromy and vanishing cycles in toric surfaces},
author = {Nick Salter},
journal= {arXiv preprint arXiv:1710.08042},
year = {2018}
}
Comments
This version incorporates a large number of improvements as suggested by a referee