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arXiv · 1701.00608

The vanishing cycles of curves in toric surfaces I

Rémi Crétois·Lionel Lang
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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.

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Rémi Crétois, Lionel Lang. 2017-01-03. The vanishing cycles of curves in toric surfaces I. https://doi.org/10.1112/s0010437x18007200

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