Desingularization of quiver Grassmannians via Nakajima categories
type: Item
instance of: scholarly article
title: Desingularization of quiver Grassmannians via Nakajima categories
zbMATH Open document ID: 1408.13059
author: Sarah Scherotzke
published in: Algebras and Representation Theory
publication date: 2017-03-07T00:00:00Z
review text: Quiver Grassmannians are varieties associated to quiver representations of a given dimension vector. They are important object in the context of additive categorification of cluster algebras. In particular, understanding the geometry and topology of such varieties is a problem that has attracted the attention of various authors. In the article under review, the author constructs a desingularization for every quiver Grassmannian associated to a standard self-injective algebra of finite representation type. The main tools used for this purpose are the so-called Nakajima categories (introduced by \textit{B. Keller} and \textit{S. Scherotzke} [J. Reine Angew. Math. 713, 85--127 (2016; Zbl 1401.14091)]), their orbit categories and their standard Frobenius models. Moreover, along the way the author also proves classification theorems about standard Frobenius models of generalized Nakajima categories.
reviewed by: Alfredo Nájera Chávez
Mathematics Subject Classification ID: 13F60
Mathematics Subject Classification ID: 16G70
Mathematics Subject Classification ID: 18E30
zbMATH DE Number: 6692652
zbMATH Keywords: Nakajima quiver varieties
zbMATH Keywords: quiver Grassmannians
zbMATH Keywords: orbit categories
MaRDI profile type: Publication
full work available at URL: s10468-016-9639-y
OpenAlex ID: W2502605478
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DOI: 10.1007/S10468-016-9639-Y
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description: scientific article; zbMATH DE number 6692652