A tropical characterization of non-archimedean algebraic varieties

We study the tropicalizations of analytic subvarieties of normal toric varieties over complete non-archimedean valuation fields. We show that a Zariski closed analytic subvariety of a normal toric variety is algebraic if its tropicalization is a finite union of polyhedra. Previously, the converse di...

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Bibliographic Details
Published in:arXiv.org 2017-06
Main Author: Mikami, Ryota
Format: Article
Language:English
Subjects:
Algebra
Complex numbers
Mathematical analysis
Toruses
Online Access:Get full text
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Summary:We study the tropicalizations of analytic subvarieties of normal toric varieties over complete non-archimedean valuation fields. We show that a Zariski closed analytic subvariety of a normal toric variety is algebraic if its tropicalization is a finite union of polyhedra. Previously, the converse direction was known by the theorem of Bieri and Groves. Over the field of complex numbers, Madani, L. Nisse, and M. Nisse proved similar results for analytic subvarieties of tori.
ISSN:2331-8422