, Volume 16, Issue 6, pp 1733-1786

Tilting Theoretical Approach to Moduli Spaces Over Preprojective Algebras

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Abstract

We apply tilting theory over preprojective algebras Λ to the study of moduli spaces of Λ-modules. We define the categories of semistable modules and give equivalences, so-called reflection functors, between them by using tilting modules over Λ. Moreover we prove that the equivalence induces an isomorphism of K-schemes between moduli spaces. In particular, we study the case when the moduli spaces are related to Kleinian singularities, and generalize some results of Crawley-Boevey (Am J Math 122:1027–1037, 2000).

Presented by: Idun Reiten.
The first author was supported by JSPS Fellowships for Young Scientists No.21-6922.
The second author was supported by JSPS Fellowships for Young Scientists No.22-5801.