The Orlik-Solomon Algebra and the Bergman Fan of a Matroid

2012/09/07 by Ilia Zharkov, Zharkov, Ilia · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO

paper · pdf · doi:10.48550/arxiv.1209.1651

7 pages, two figures, journal version

openalex publication_date 2012/09/07 · arxiv created 2013/10/08 · arxiv updated 2013/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a matroid M one can define its Orlik-Solomon algebra OS(M) and the Bergman fan Σ₀(M). On the other hand to any rational polyhedral fan Σ one can associate its tropical homology and cohomology groups \F_\bullet(Σ), \F^\bullet (Σ). We will show that the projective Orlik-Solomon algebra OS₀(M) is canonically isomorphic to \F^\bullet (Σ₀(M)).

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