DEFORMATION QUANTIZATION AND PERVERSE SHEAVES
Abstract
Kashiwara, Polesello, Schapira and D'Agnolo defined canonical deformation quantizations of a holomorphic symplectic manifold and a holomorphic Lagrangian submanifold equipped with an orientation data. The goal of this paper is to use deformation quantization modules to construct a Fukaya-like category of holomorphic Lagrangians, resolving a conjecture of Joyce. Our main result describes the RHom complex between two such deformation quantization modules associated to a pair of Lagrangian submanifolds in terms of the derived geometry of the Lagrangian intersection. Namely, we identify the RHom complex with the DT sheaf associated to the d-critical structure on the Lagrangian intersection. Via a Riemann-Hilbert correspondence this describes the RHom complex in the category of microsheaves of sheaf quantizations of conic holomorphic Lagrangians.
Fields of Study & Subjects
Geometry and complex manifolds
Homotopy and Cohomology in Algebraic Topology
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 6
- Pages
- 1067-1161
- Publication date
- 15 April 2026
- Language
- EN