Mixed volumes of normal complexes
Combinatorics
2023-01-16 v1 Algebraic Geometry
Abstract
Normal complexes are orthogonal truncations of polyhedral fans. In this paper, we develop the study of mixed volumes for normal complexes. Our main result is a sufficiency condition that ensures when the mixed volumes of normal complexes associated to a given fan satisfy the Alexandrov-Fenchel inequalities. By specializing to Bergman fans of matroids, we give a new proof of the Heron-Rota-Welsh Conjecture as a consequence of the Alexandrov-Fenchel inequalities for normal complexes.
Keywords
Cite
@article{arxiv.2301.05278,
title = {Mixed volumes of normal complexes},
author = {Lauren Nowak and Patrick O'Melveny and Dustin Ross},
journal= {arXiv preprint arXiv:2301.05278},
year = {2023}
}
Comments
37 pages, 17 images, comments welcome