On the quiver Grassmannian in the acyclic case

• Autores: Philippe Caldero, Markus Reineke
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 11, 2008, págs. 2369-2380
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2008.03.025
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial cardinality and we give different approaches to Euler characteristics. Our main result is the positivity of Euler characteristics when M is an exceptional module. This solves a conjecture of Fomin and Zelevinsky for acyclic cluster algebras.