Cohomological decomposition of compact complex manifolds and holomorphic deformations

Latorre, A. (Universidad de Zaragoza) ; Ugarte, L. (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1090/proc/13244

Año: 2017

Publicado en: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 145, 1 (2017), 335-353
ISSN: 0002-9939

Factor impacto JCR: 0.707 (2017)

Categ. JCR: MATHEMATICS rank: 153 / 309 = 0.495 (2017) - Q2 - T2
Categ. JCR: MATHEMATICS, APPLIED rank: 178 / 252 = 0.706 (2017) - Q3 - T3

Factor impacto SCIMAGO: 1.183 - Mathematics (miscellaneous) (Q1) - Applied Mathematics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28326-C02-01
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2014-58616-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)