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Stability conditions and Kleinian singularities. (English) Zbl 1228.14012
Summary: We describe (connected components of) 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 of stability conditions are covering spaces of regular subsets of the corresponding complexified Cartan algebras.

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14B05 Singularities in algebraic geometry
14E16 McKay correspondence
18E30 Derived categories, triangulated categories (MSC2010)
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