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

2005/03/04 by Frederic Chapoton, Chapoton, Frederic
Mathematics · #14F25 #16G20 #17B20 #FOS: Mathematics #MSC2000 : 14M25 #Quantum Algebra (math.QA) #math.QA #msc:14F25 #msc:14M25 #msc:16G20 #msc:17B20 #msc:MSC2000

paper · pdf · doi:10.48550/arxiv.math/0503077

12 pages

arxiv created 2005/03/04 · arxiv updated 2009/12/01

Abstract

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.

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