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On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends our previous results in which the symplectic manifold was compact. The main tool is a finiteness theorem for R-constructible sheaves on a real analytic manifold in a non proper situation.
We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation spaces are as f
On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $mathcal{M}mapstomathcal{M}_{mathrm{reg}}$, called regularization. Recall that $mathcal{M}_{mathrm{r
We prove the following two results 1. For a proper holomorphic function $ f : X to D$ of a complex manifold $X$ on a disc such that ${df = 0 } subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric (a,b)-module $E
This paper is a survey of finiteness results in hyperkahler geometry. We review some classical theorems by Sullivan, Kollar-Matsusaka, Huybrechts, as well as theorems in the recent literature by Charles, Sawon, and joint results of the author with Ve
The formality theorem for Hochschild chains of the algebra of functions on a smooth manifold gives us a version of the trace density map from the zeroth Hochschild homology of a deformation quantization algebra to the zeroth Poisson homology. We prop