On the quiver Grassmannian in the acyclic case

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
Minor corrections. References added

Keywords

Representation Theory, Algebraic Geometry, 16G20, 14L30, 16G70

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/123570

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611074
 http://arxiv.org/abs/math/0611074

Collections

arXiv