Stacks of quantization-deformation modules on complex symplectic manifolds

By P. Polesello, P. Schapira. 2003

68 citations recorded by the source corpus.

On a complex symplectic manifold X, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter τ, a substitute to the lack of homogeneity. We also quantize involutive submanifolds of contact manifolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/66ec00134c34cf78fcd027e2aa83799bc20ed415

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On global deformation quantization in the algebraic case (2006, background): “Let U be as above and let u be the linear category with objects ∅ ( J ⊂ {1, . . . , n} and u(J, J ′) = { HomOX (j∗OUJ , j∗OUJ′ ) = OX(UJ′) if J ⊂ J ′ 0 otherwise where j : UJ → X denotes the inclusion map.”
Microlocal theory of sheaves and Tamarkin's non displaceability theorem (2011, background): “This trick appears for example in the complex case in [10] where a deformation quantization ring (with an ~-parameter) is constructed on the cotangent bundle T X to a complex manifold X by using the ring of microdifferential operators of [11] on T (X × C).”
Microlocalization of rational Cherednik algebras (2007, background): “We refer the reader to [24] (where the convergent version is studied, while we use the simpler formal version).”
Constructible sheaves and the Fukaya category (2006, background): “(See for example Kontsevich [24], Kashiwara [18], or Polesello-Schapira [30].)”