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math.AG2025
Fano compactifications of mutation algebras
Joshua Enwright, Luca Francone, JoaquÃn Moraga +1
In this article, we introduce the notion of mutation semigroup algebras. This concept simultaneously generalizes cluster algebras and semigroup algebras. We show that, under some m…
math.AG2025
Intersection multiplicity one for the Belkale-Kumar product in G/B
Nicolas Ressayre, Luca Francone
Consider the complete flag variety of a complex semisimple algebraic group . We show that the structure coefficients of the Belkale-Kumar product , on the cohomolog…
math.AG2024
Cluster structures on Cox rings
Luca Francone
We construct a graded cluster algebra structure on the Cox ring of a smooth complex variety , depending on a base cluster structure on the ring of regular functions of an open s…