Classification of normal toric varieties over a valuation ring of rank one
Walter Gubler
Fakultät für Mathematik Department of Mathematics Universität Regensburg KU Leuven Universitätsstrasse 31 Celestijnenlaan 200B D-93040 Regensburg B-3001 HeverleeAlejandro Soto
Fakultät für Mathematik Department of Mathematics Universität Regensburg KU Leuven Universitätsstrasse 31 Celestijnenlaan 200B D-93040 Regensburg B-3001 Heverlee
![Classification of normal toric varieties over a valuation ring of rank one cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-dm-volume-20.png&w=3840&q=90)
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.
Cite this article
Walter Gubler, Alejandro Soto, Classification of normal toric varieties over a valuation ring of rank one. Doc. Math. 20 (2015), pp. 171–198
DOI 10.4171/DM/488