The vanishing cycles of curves in toric surfaces I

Abstract

This article is the first in a series of two in which we study the vanishing cycles of curves in toric surfaces. We give a list of possible obstructions to contract vanishing cycles within a given complete linear system. Using tropical means, we show that any non-separating simple closed curve is a vanishing cycle whenever none of the listed obstructions appears.

46 pages, 15 figures, minor corrections, reference added

References in corpus (2)

• The vanishing cycles of curves in toric surfaces I
• On the monodromy group of the family of smooth plane curves

Cited by in corpus (6)

• Galois theory for general systems of polynomial equations
• The vanishing cycles of curves in toric surfaces I
• Minimal bipartite dimers and higher genus Harnack curves
• Monodromy of rational curves on toric surfaces
• A note on the Severi problem for toric surfaces
• The Moduli Space of Harnack Curves in Toric Surfaces