Dynkin diagrams and crepant resolutions of quotient singularities

1999/03/27 by D. Kaledin, Kaledin, D.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9903157

30 pages, LaTeX2e

arxiv created 1999/03/27 · arxiv updated 2009/11/30

Abstract

Let V be a complex vector space on which a finite group G acts by linear transformations. Let W = V ⊕ V^* be the sum of V with its dual V^*. We prove that if the quotient W/G admits a smooth crepant resolution, then the subgroup G ⊂ Aut V is generated by complex reflections. We also obtain some results on the structure of smooth crepant resolutions of the quotients W/G, where W is a symplectic vector space, and G ⊂ Aut W is a finite group of symplectic linear transformations of the vector space W.

Related

• Holomorphic symplectic geometry and orbifold singularities
• Partial resolutions of Hilbert type, Dynkin diagrams, and generalized Kummer varieties
• McKay correspondence for symplectic quotient singularities
• On the (non)existence of symplectic resolutions for imprimitive symplectic reflection groups
• On smoothness of minimal models of quotient singularities by finite subgroups of SL_n(ℂ)