On the invariant theory for acyclic gentle algebras

Carroll, Andrew; Chindris, Calin

doi:10.1090/S0002-9947-2014-06191-6

On the invariant theory for acyclic gentle algebras
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by Andrew T. Carroll and Calin Chindris PDF

Trans. Amer. Math. Soc. 367 (2015), 3481-3508 Request permission

Abstract:

In this paper we show that the fields of rational invariants over the irreducible components of the module varieties for an acyclic gentle algebra are purely transcendental extensions. Along the way, we exhibit for such fields of rational invariants a transcendence basis in terms of Schofield’s determinantal semi-invariants.

We also show that moduli spaces of modules over regular irreducible components are just products of projective spaces.

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