On quantization of complex symplectic manifolds

Abstract

Let X be a complex symplectic manifold. By showing that any Lagrangian subvariety has a unique lift to a contactification, we associate to X a triangulated category of regular holonomic microdifferential modules. If X is compact, this is a Calabi-Yau category of complex dimension dim X+1. We further show that regular holonomic microdifferential modules can be realized as modules over a quantization algebroid canonically associated to X.

38 pages

References in corpus (5)

• Deformation quantization modules
• Branes and Quantization
• Stacks of quantization-deformation modules on complex symplectic manifolds
• Oscilatory modules
• A note on quantization of complex symplectic manifolds

Cited by in corpus (2)

• Morita classes of microdifferential algebroids
• Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties