Hodge theory for tropical fans
Combinatorics
2023-10-25 v1 Algebraic Geometry
Abstract
This paper is the first in a series devoted to the development of a Hodge theory for tropical varieties. We introduce a notion of T-stability for tropical fans and prove that various geometric properties of tropical fans are T-stable. As a consequence, we establish K\"ahler properties for the Chow ring in a large class of tropical fans, going beyond the case of matroids and their Bergman fans. As a by-product, we obtain a new proof of the K\"ahler package for combinatorial geometries. The approach makes it possible to deal with tropical fans with general weights.
Keywords
Cite
@article{arxiv.2310.15367,
title = {Hodge theory for tropical fans},
author = {Omid Amini and Matthieu Piquerez},
journal= {arXiv preprint arXiv:2310.15367},
year = {2023}
}
Comments
68 pages, 4 figures. Comments welcome! arXiv admin note: substantial text overlap with arXiv:2105.01504