doi:10.1090/proc/13244engLatorre, A.Ugarte, L.Cohomological decomposition of compact complex manifolds and holomorphic deformationsART-2017-97052The 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.2017http://zaguan.unizar.es/record/5778510.1090/proc/13244http://zaguan.unizar.es/record/57785oai:zaguan.unizar.es:57785info:eu-repo/grantAgreement/ES/DGA/E15info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28326-C02-01info:eu-repo/grantAgreement/ES/MINECO/MTM2014-58616-PPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 145, 1 (2017), 335-353All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess