2024/05/08 by Omid Amini, Amini, Omid, Matthieu Piquerez +1
Earth and Planetary Sciences · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Cryospheric studies and observations #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2405.05014
openalex publication_date 2024/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the Chow ring of any simplicial fan is isomorphic to the middle degree part of the tropical cohomology ring of its canonical compactification. Using this result, we prove a tropical analogue of Kleiman's criterion of ampleness for fans. In the case of tropical fans that are homology manifolds, we obtain an isomorphism between the Chow ring of the fan and the entire tropical cohomology of the canonical compactification. When applied to matroids, this provides a new representation of the Chow ring of a matroid as the cohomology ring of a projective tropical manifold.