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The vanishing cycles of curves in toric surfaces I
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden.
2018 (English)In: Compositio Mathematica, ISSN 0010-437X, E-ISSN 1570-5846, Vol. 154, no 8, p. 1659-1697Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2018. Vol. 154, no 8, p. 1659-1697
Keywords [en]
tropical geometry, toric varieties and Newton polygons, vanishing cycles and monodromy, simple Harnack curves
National Category
Geometry
Identifiers
URN: urn:nbn:se:uu:diva-363055DOI: 10.1112/S0010437X18007200ISI: 000440858600004OAI: oai:DiVA.org:uu-363055DiVA, id: diva2:1257020
Funder
Knut and Alice Wallenberg FoundationAvailable from: 2018-10-18 Created: 2018-10-18 Last updated: 2018-10-18Bibliographically approved

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