Monodromy and vanishing cycles in toric surfaces

2017/10/22 by Salter, Nick · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1710.08042

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.

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• Monodromy and vanishing cycles for sufficiently ample linear systems on simply connected surfaces
• Exotic knottings and symmetries of surfaces in 4-manifolds

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