3 papers
math.AG2025
Cohomologically tropical varieties
Edvard Aksnes, Omid Amini, Matthieu Piquerez +1
Given the tropicalization of a complex subvariety of the torus, we define a morphism between the tropical cohomology and the rational cohomology of their respective tropical compac…
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…