On the quiver Grassmannian in the acyclic case
Representation Theory
2007-05-23 v2 Algebraic Geometry
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.
Cite
@article{arxiv.math/0611074,
title = {On the quiver Grassmannian in the acyclic case},
author = {Philippe Caldero and Markus Reineke},
journal= {arXiv preprint arXiv:math/0611074},
year = {2007}
}
Comments
Minor corrections. References added