English

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.

Keywords

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

R2 v1 2026-06-22T22:22:06.491Z