Perverse coherent sheaves on symplectic singularities

TL;DR

This paper introduces perverse coherent sheaves tailored for symplectic singularities, establishing their properties and demonstrating their role as a basis in the Grothendieck group, with applications to nilpotent cones and affine Grassmannians.

Contribution

It defines a new class of sheaves for symplectic singularities and connects them to existing structures like nilpotent cones and affine Grassmannians.

Findings

Perverse coherent sheaves form a basis in the Grothendieck group of Poisson sheaves.

The construction applies to nilpotent cones and affine Grassmannians as special cases.

Properties of these sheaves are systematically studied.

Abstract

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck group of Poisson sheaves. We show that perverse coherent bases for the nilpotent cone and for the affine Grassmannian arise as particular cases of our construction.