On the quiver Grassmannian in the acyclic case |
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Authors: | Philippe Caldero Markus Reineke |
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Institution: | a Institut Camille Jordan, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France b Fachbereich C, Bergische Universität Wuppertal, D - 42097 Wuppertal, Germany |
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Abstract: | 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. |
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Keywords: | 14L30 17B37 |
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