On the quiver Grassmannian in the acyclic case

Details On the quiver Grassmannian in the acyclic case On the quiver Grassmannian in the acyclic case

2006-11-03

arxiv.org/abs/math/0611074v2

Mathematics

Representation Theory

Minor corrections. References added

Scientific paper

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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