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Aspects of Geometric Quantization Theory in Poisson Geometry

Izu Vaisman (2000)

Banach Center Publications

This is a survey exposition of the results of [14] on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the results of [13] on a certain kind of super-geometric quantization. A general formulation of the geometric quantization problem is given at the beginning.

Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles

Robert Berman, Johannes Sjöstrand (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.

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