Classification of normal toric varieties over a valuation ring of rank one
Algebraic Geometry
2015-01-30 v2 Number Theory
Abstract
Normal toric varieties over a field or a discrete valuation ring are classified by rational polyhedral fans. We generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one. The proof is based on a generalization of Sumihiro's theorem to this non-noetherian setting. These toric varieties play an important role for tropicalizations.
Keywords
Cite
@article{arxiv.1303.1987,
title = {Classification of normal toric varieties over a valuation ring of rank one},
author = {Walter Gubler and Alejandro Soto},
journal= {arXiv preprint arXiv:1303.1987},
year = {2015}
}
Comments
22 pages. Minor modifications after the comments of the referee. Accepted by Documenta Mathematica