Moduli spaces of modules of Schur-tame algebras

2014/07/29 by Andrew T. Carroll, Carroll, Andrew T., Calin Chindris +1 · 1 citation
Mathematics · Physics and Astronomy · #16G10 #16G30 #16G60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1407.7775

openalex publication_date 2014/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 theta-stable irreducible component C of a module variety of A-modules, the moduli space of theta-semi-stable points of C is either a point or a rational projective curve.

Citations

• Wild Algebras: Two Examples
• Generic Modules for string algebras

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