Faithful tropicalisation and torus actions
Algebraic Geometry
2017-10-10 v3 Combinatorics
Abstract
For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, H\"abich, and Werner), matrix varieties defined by the vanishing of 3 times 3 minors, and for the hypersurface defined by Cayley's hyperdeterminant.
Cite
@article{arxiv.1404.4715,
title = {Faithful tropicalisation and torus actions},
author = {Jan Draisma and Elisa Postinghel},
journal= {arXiv preprint arXiv:1404.4715},
year = {2017}
}
Comments
22 pages, 6 figures, corrected in an error in proposition 4.2---many thanks to a referee! Also corrected a latex-problem with references