20 citations · 44 across the 7 of their papers we have counts for
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On quantizations of complex contact manifolds
Pietro Polesello
A (holomorphic) quantization of a complex contact manifold is a filtered algebroid stack which is locally equivalent to the ring E of microdifferential operators and which has triv…
Morita classes of microdifferential algebroids
Andrea D'Agnolo, Pietro Polesello
Projective cotangent bundles of complex manifolds are the local models of complex contact manifolds. Such bundles are quantized by the algebra of microdifferential operators (a loc…
Classification of deformation quantization algebroids on complex symplectic manifolds
Pietro Polesello
Deformation quantization algebroids over a complex symplectic manifold X are locally given by rings of WKB operators, that is, microdifferential operators with an extra central par…
Deformation-Quantization of Complex Involutive Submanifolds
Andrea D'Agnolo, Pietro Polesello
The sheaf of rings of WKB operators provides a deformation-quantization of the cotangent bundle to a complex manifold. On a complex symplectic manifold there may not exist a sh…
Stacks of twisted modules and integral transforms
Andrea D'Agnolo, Pietro Polesello
Stacks were introduced by Grothendieck and Giraud and are, roughly speaking, sheaves of categories. Kashiwara developed the theory of twisted modules, which are objects of stacks l…
Stacks of quantization-deformation modules on complex symplectic manifolds
Pietro Polesello, Pierre Schapira
On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parame…