On the quiver Grassmannian in the acyclic case

被引：56

作者：

Caldero, Philippe ^{[1
]}

Reineke, Markus ^{[2
]}

机构：

[1] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France

[2] Berg Univ Wuppertal, Fachbereich C, D-42097 Wuppertal, Germany

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2008年 / 212卷 / 11期

关键词：

D O I：

10.1016/j.jpaa.2008.03.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：2369 / 2380

页数：12

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