On moduli spaces for quasitilted algebras.
type: Item
instance of: scholarly article
title: On moduli spaces for quasitilted algebras.
zbMATH Open document ID: 1319.16014
author: Grzegorz Bobiński
published in: Algebra \& Number Theory
publication date: 2014-10-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1312.5470
reviewed by: Matyas Domokos
Mathematics Subject Classification ID: 16G10
Mathematics Subject Classification ID: 16G60
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 14L24
zbMATH DE Number: 6353691
zbMATH Keywords: finite dimensional algebras
zbMATH Keywords: quasitilted algebras
zbMATH Keywords: moduli spaces
zbMATH Keywords: semi-invariants
zbMATH Keywords: tame algebras
MaRDI profile type: Publication
OpenAlex ID: W3103596368
arXiv ID: 1312.5470
DOI: 10.2140/ANT.2014.8.1521
Wikidata QID: Q131317196
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review text: The paper contributes to the program of characterizing classes of finite dimensional algebras -- originally defined in terms of module theory -- by geometric properties of associated algebraic varieties parametrizing modules over the algebra. An algebra \(\Lambda\) is called quasitilted if \(\Lambda\) is the endomorphism algebra of a tilting object in a connected hereditary abelian \(k\)-category with finite-dimensional homomorphism and extension spaces.NEWLINENEWLINE The main result of the paper is that every tame quasitilted algebra \(\Lambda\) satisfies the following property: for any dimension vector \(d\), for any connected component \(C\) of the variety of \(d\)-dimensional \(\Lambda\)-modules, and any weight \(\theta\) such that \(C\) contains a \(\theta\)-semistable point, the moduli space \(M(C)^{ss}_\theta\) of \(\theta\)-semistable points in \(C\) is a product of projective spaces. -- Note that together with earlier results of \textit{C. Chindris} [Algebra Number Theory 7, No. 1, 193-214 (2013; Zbl 1297.16016)] this gives a characterization of tameness for quasitilted algebras.
description: scientific article; zbMATH DE number 6353691