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Cohomological decomposition of compact complex manifolds and holomorphic deformations


Authors: Adela Latorre and Luis Ugarte
Journal: Proc. Amer. Math. Soc. 145 (2017), 335-353
MSC (2010): Primary 32G05, 53C15, 53C56, 58A12, 22E25
DOI: https://doi.org/10.1090/proc/13244
Published electronically: August 1, 2016
MathSciNet review: 3565385
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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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Additional Information

Adela Latorre
Affiliation: Departamento de Matemáticas-I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
Email: adela@unizar.es

Luis Ugarte
Affiliation: Departamento de Matemáticas-I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
Email: ugarte@unizar.es

DOI: https://doi.org/10.1090/proc/13244
Keywords: De Rham cohomology, complex structure, solvmanifold, holomorphic deformation
Received by editor(s): October 6, 2015
Received by editor(s) in revised form: April 5, 2016
Published electronically: August 1, 2016
Communicated by: Franc Forstneric
Article copyright: © Copyright 2016 American Mathematical Society