Andrew T. Carroll, Calin Chindris
Published 2014-07-29Version 1
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.
Comments: arXiv admin note: text overlap with arXiv:1210.3579
On the invariant theory for acyclic gentle algebras
Irreducible components of the Jordan varieties
$\mathscr{A}=\mathscr{U}$ for cluster algebras from moduli spaces of $G$-local systems
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