http://swrc.ontoware.org/ontology#UnrefereedArticle
A Tropical Characterization of Algebraic Subvarieties of Toric Varieties over Non-Archimedean Fields
en
Tropical geometry
rigid analytic geometry
Mikami Ryota
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.
Journal of Mathematical Sciences The University of Tokyo
25
2
129-147
2018-06-29
13405705
AA11021653
Graduate School of Mathematical Sciences, The University of Tokyo