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No abstract uploaded!

No abstract uploaded!

We introduce the notions of strong local Torelli and T-class for polarized manifolds, and prove that strong local Torelli implies global Torelli theorem on the Torelli spaces for polarized manifolds in the T-class. We discuss many new examples of projective manifolds for which such global Torelli theorem holds. As applications we prove that, in these cases, a canonical completion of the Torelli space is a bounded pseudoconvex domain in complex Euclidean space, and show that generic Torelli implies global Torelli on moduli space with certain level structure.

It is shown that the Bargmann-Fock spaces of entire functions, A^{p}(C),$p$≧1 have a bounded unconditional basis of Wilson type [DJJ] which is closely related to the reproducing kernel. From this is derived a new sampling and interpolation result for these spaces.