| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4597944 | Journal of Pure and Applied Algebra | 2008 | 12 Pages |
Abstract
Let AA be the path algebra of a quiver QQ with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given AA-module MM. 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 MM is an exceptional module. This solves a conjecture of Fomin and Zelevinsky for acyclic cluster algebras.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Philippe Caldero, Markus Reineke,