Deformation Openness and Closedness of Various Classes of Compact Complex Manifolds; Examples

Details Deformation Openness and Closedness of Various Classes of Compact Complex Manifolds; Examples Deformation Openness and Closedness of Various Classes of Compact Complex Manifolds; Examples

2011-02-08

arxiv.org/abs/1102.1687v1

Mathematics

Algebraic Geometry

48 pages

Scientific paper

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (K\"ahler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the Fr\"olicher spectral sequence, as well as the behaviour of these properties under holomorphic deformations. The emphasis will be placed on the notion of {\it strongly Gauduchon} (sG) manifolds that we introduced recently in the study of deformation limits of projective and Moishezon manifolds. Various examples of sG and non-sG manifolds are exhibited while a range of constructions already known in the literature are reviewed and reinterpreted from this new standpoint.

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