5 papers
An introduction to -bands
Luca Francone, Bernard Leclerc
We give an introduction to our results on cluster structures for schemes of -bands emphasizing their connections with seminal works of Frenkel and Reshetikhin in the 90's. I…
Cluster structures on schemes of bands
Luca Francone, Bernard Leclerc
We introduce new objects, called -bands, associated with a simple simply-connected algebraic group , and a Coxeter element in its Weyl group. We show that bands of a…
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…
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…
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…