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Register a new userNote on the semi-continuity of the algebraic dimension
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Authors
Daniel Barlet
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In this short Note we show that the direct image sheaf R 1 $pi$ * (O X) associated to an analytic family of compact complex manifolds $pi$ : X $rightarrow$ S parametrized by a reduced complex space S is a locally free (coherent) sheaf of O S --modules. This result allows to improve a semi-continuity type result for the algebraic dimension of compact complex manifolds in an analytic family given in [B.15]. AMS Classification 2010. 32G05-32A20-32J10.
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In this paper, we prove the semi-continuity theorem of Diederich-Forn{ae}ss index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.
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