Moduli Spaces of Modules of Schur-Tame Algebras

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• 作者：Andrew T. Carroll ; Calin Chindris
• 关键词：Schur ; tame algebras ; Moduli spaces of modules ; String algebras ; 16G10 ; 16G60 ; 16R30
• 刊名：Algebras and Representation Theory
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：18
• 期：4
• 页码：961-976
• 全文大小：409 KB
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• 作者单位：Andrew T. Carroll (1)
  Calin Chindris (1)
  
  1. Mathematics Department, University of Missouri-Columbia, Columbia, MO, 65211, USA
  
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079

文摘

In this paper, we first show that for an acyclic gentle algebra A, the irreducible components of any moduli space of A-modules are products of projective spaces. Next, we show that the nice geometry of the moduli spaces of modules of an algebra does not imply the tameness of the representation type of the algebra in question. Finally, we place these results in the general context of moduli spaces of modules of Schur-tame algebras. More specifically, we show that for an arbitrary Schur-tame algebra A and 饾渻-stable irreducible component C of a module variety of A-modules, the moduli space \(\mathcal {M}(C)^{ss}_{\theta }\) is either a point or a rational projective curve.