Localization theorems for quantized symplectic resolutions

Abstract

The goal of this paper is to establish Beilinson-Bernstein type localization theorems for quantizations of some conical symplectic resolutions. We prove the full localization theorems for finite and affine type A Nakajima quiver varieties. The proof is based on two partial results that hold in more general situations. First, we establish an exactness result for global section functor if there is a tilting generator that has a rank 1 summand. Second, we examine when the global section functor restricts to an equivalence between categories $\mathcal{O}$.

54 pages

References in corpus (3)

• Line bundles over Coulomb branches
• Coherent sheaves and quantum Coulomb branches I: tilting bundles from integrable systems
• On modular categories O for quantized symplectic resolutions