The vanishing cycles of curves in toric surfaces I
Rémi Crétois, Lionel Lang · Compositio Mathematica · 2018
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.