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math.AG2024
Homological smoothness and Deligne resolution for tropical fans
Omid Amini, Matthieu Piquerez
We say that a tropical fan is homologically smooth if each of its open subsets verify tropical Poincare duality. A tropical homology manifold is a tropical variety that is locally…
math.AG2024
Tropical Feichtner-Yuzvinsky and positivity criterion for fans
Omid Amini, Matthieu Piquerez
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 p…
math.AG2024
Tropicalization of linear series and tilings by polymatroids
Omid Amini, Eduardo Esteves
We show that tropicalization of linear series on curves gives rise to two-parameter families of tilings by polymatroids, with one parameter arising from the theory of divisors on t…