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The vanishing cycles of curves in toric surfaces I

Part of: Singularities Special varieties

Published online by Cambridge University Press:  18 July 2018

Rémi Crétois  and
Lionel Lang
Rémi Crétois
Affiliation:
Matematiska Institutionen, Uppsala Universitet, Box 480, 751 06 Uppsala, Sweden email [email protected]
Lionel Lang
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden email [email protected]
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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.

Keywords

tropical geometrytoric varieties and Newton polygonsvanishing cycles and monodromysimple Harnack curves

MSC classification

Primary: 14T05: Tropical geometry 14M25: Toric varieties, Newton polyhedra 32S30: Deformations of singularities; vanishing cycles
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 8 , August 2018 , pp. 1659 - 1697
Copyright
© The Authors 2018 

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