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Inventiones mathematicae

, Volume 194, Issue 3, pp 515–534 | Cite as

Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics

  • Dan Popovici
Article

Abstract

This paper is intended to start a series of works aimed at proving that if in a (smooth) complex analytic family of compact complex manifolds all the fibres, except one, are supposed to be projective, then the remaining (limit) fibre must be Moishezon. A new method of attack, whose starting point originates in Demailly’s work, is introduced. While we hope to be able to address the general case in the near future, two important special cases are established here: the one where the Hodge numbers h 0,1 of the fibres are supposed to be locally constant and the one where the limit fibre is assumed to be a strongly Gauduchon manifold. The latter is a rather weak metric assumption giving rise to a new, rather general, class of compact complex manifolds that we hereby introduce and whose relevance to this type of problems we underscore.

Keywords

Manifold Hodge Number Compact Complex Manifold Projective Manifold Compact Complex Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Institut de Mathématiques de ToulouseUniversité Paul SabatierToulouseFrance

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