Cohomology rings of toric varieties assigned to cluster quivers: the case of unioriented quivers of type A

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

The theory of cluster algebras of S. Fomin and A. Zelevinsky has assigned a fan to each Dynkin diagram. Then A. Buan, R. Marsh, M. Reineke, I. Reiten and G. Todorov have generalized this construction using arbitrary quivers on Dynkin diagrams. In the special case of the unioriented quiver of type A, we describe the cohomology ring of the toric variety associated to this fan. A natural base is obtained and an explicit rule is given for the product of any two generators.

Mots clés: toric variety; quiver; cluster algebra; cohomology

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. Cohomology rings of toric varieties assigned to cluster quivers: the case of unioriented quivers of type A. 2005. ⟨hal-00004356⟩