Higher convexity for complements of tropical varieties
Algebraic Geometry
2015-07-09 v3 Combinatorics
Abstract
We consider Gromov's homological higher convexity for complements of tropical varieties, establishing it for complements of tropical hypersurfaces and curves, and for nonarchimedean amoebas of varieties that are complete intersections over the field of complex Puiseaux series. Based on these results, we conjecture that the complement of a tropical variety has this higher convexity, and we prove a weak form of our conjecture for the nonarchimedean amoeba of a variety over the complex Puiseaux field. One of our main tools is Jonsson's limit theorem for tropical varieties.
Keywords
Cite
@article{arxiv.1411.7363,
title = {Higher convexity for complements of tropical varieties},
author = {Mounir Nisse and Frank Sottile},
journal= {arXiv preprint arXiv:1411.7363},
year = {2015}
}
Comments
11 pages