On Quantization of Complex Symplectic Manifolds

  • Andrea D’AgnoloEmail author
  • Masaki Kashiwara


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.


Manifold Complex Manifold Symplectic Manifold Deformation Quantization Contact Manifold 
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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di PadovaPadovaItaly
  2. 2.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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