Functorial tropicalization of logarithmic schemes: The case of constant coefficients
Algebraic Geometry
2017-06-14 v4
Abstract
The purpose of this article is to develop foundational techniques from logarithmic geometry in order to define a functorial tropicalization map for fine and saturated logarithmic schemes in the case of constant coefficients. Our approach crucially uses the theory of fans in the sense of K. Kato and generalizes Thuillier's retraction map onto the non-Archimedean skeleton in the toroidal case. For the convenience of the reader many examples as well as an introductory treatment of the theory of Kato fans are included.
Keywords
Cite
@article{arxiv.1310.6269,
title = {Functorial tropicalization of logarithmic schemes: The case of constant coefficients},
author = {Martin Ulirsch},
journal= {arXiv preprint arXiv:1310.6269},
year = {2017}
}
Comments
v4: 33 pages. Restructured introduction, otherwise minor changes. To appear in the Proceedings of the LMS