A Parameterization of D equivalences of coherent sheaves of symplectic resolutions of a given symplectic singularity

2016/01/11 by Boger, Dorin
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.02448

Abstract

Let G be a reductive groups over an algebraically closed field k. Let P⁽ⁱ⁾ be associated parabolic subgroups, and X⁽ⁱ⁾:=T^*G/Pⁱ. The bounded derived categories of coherent sheaves on X⁽ⁱ⁾ are equivalent, but there is no canonical equivalence. By refining a construction from a previous paper, we construct a local system of categories over a topological space V⁰_C, where these categories are assigned to different points in V⁰_C. Natural equivalence functors between these categories are parameterized by homotopy classes of paths between the corresponding points.

Related

• Groups actions, and D equivalences of categories of coherent sheaves of symplectic resolutions
• McKay equivalence for symplectic resolutions of singularities
• Pointwise purity, derived Satake, and Symplectic duality
• Reconstruction theorems in the supported case
• Derived equivalences by quantization