Cohomological decomposition of compact complex manifolds and holomorphic deformations

Latorre, Adela; Ugarte, Luis

doi:10.1090/proc/13244

Cohomological decomposition of compact complex manifolds and holomorphic deformations
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Proc. Amer. Math. Soc. 145 (2017), 335-353 Request permission

Abstract:

The main goal of this note is the study of pureness and fullness properties of compact complex manifolds under holomorphic deformations. Firstly, we construct small deformations of pure-and-full complex manifolds along which one of these properties is lost while the other one is preserved. Secondly, we show that the property of being pure-and-full is not closed under holomorphic deformations. In order to do so, we focus on the class of 6-dimensional solvmanifolds endowed with invariant complex structures. In the special case of nilmanifolds, we also give a classification of those invariant complex structures that are both pure and full. In addition, relations of the cohomological decomposition with other metric and complex properties are studied.

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