Mixed volumes of normal complexes

2023/01/12 by Lauren Nowak, Nowak, Lauren, Patrick O’Melveny +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2301.05278

openalex publication_date 2023/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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