Stability conditions and Kleinian singularities

Details Stability conditions and Kleinian singularities Stability conditions and Kleinian singularities

2005-08-15

arxiv.org/abs/math/0508257v2

Mathematics

Algebraic Geometry

Results unchanged, several mistakes in the proof corrected

Scientific paper

We describe the spaces of stability conditions on certain triangulated categories associated to Dynkin diagrams. These categories can be defined either algebraically via module categories of preprojective algebras, or geometrically via coherent sheaves on resolutions of Kleinian singularities. The resulting spaces are related to regular subsets of the corresponding complexified Cartan algebras.

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