Higher Connectivity of Tropicalizations
Algebraic Geometry
2021-09-23 v2 Combinatorics
Abstract
We show that the tropicalization of an irreducible d-dimensional variety over a field of characteristic 0 is (d-l)-connected through codimension one, where l is the dimension of the lineality space of the tropicalization. From this we obtain a higher connectivity result for skeleta of rational polytopes. We also prove a tropical analogue of the Bertini Theorem: the intersection of the tropicalization of an irreducible variety with a generic hyperplane is again the tropicalization of an irreducible variety.
Cite
@article{arxiv.1908.05988,
title = {Higher Connectivity of Tropicalizations},
author = {Diane Maclagan and Josephine Yu},
journal= {arXiv preprint arXiv:1908.05988},
year = {2021}
}
Comments
Simplified proof of Theorem 5, plus other minor edits