Tilting theoretical approach to moduli spaces over preprojective algebras

Details Tilting theoretical approach to moduli spaces over preprojective algebras Tilting theoretical approach to moduli spaces over preprojective algebras

2010-08-26

arxiv.org/abs/1008.4451v3

Mathematics

Algebraic Geometry

31pages, 1 figure. The title is changed. The paper, mainly Section 4, is improved in a more general setting

Scientific paper

We apply tilting theory over preprojective algebras $Lambda$ to a study of moduli space of $Lambda$-modules. We define the categories of semistable modules and give an equivalence, so-called reflection functors, between them by using tilting modules over $Lambda$. Moreover we prove that the equivalence induces an isomorphism of algebraic varieties between moduli spaces. In particular, we study in the case when the moduli spaces related to the Kleinian singularity. We generalize a result of Crawley-Boevey which is known another proof of the McKay correspondence of Ito-Nakamura type.

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