Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Angella - N. Tardini

Quantitative and qualitative cohomological properties for non-K\"ahler manifolds

created by daniele on 12 Jan 2016
modified on 17 Nov 2017


Published Paper

Inserted: 12 jan 2016
Last Updated: 17 nov 2017

Journal: Proc. Amer. Math. Soc.
Volume: 145
Number: 1
Pages: 273-285
Year: 2017
Doi: 10.1090/proc/13209

ArXiv: 1507.07108 PDF
Links: arXiv:1507.07108


We introduce a "qualitative property" for Bott-Chern cohomology of complex non-K\"ahler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the validity of the $\partial\overline\partial$-Lemma. This follows from a quantitative study of Bott-Chern cohomology. In this context, we also prove a new bound on the dimension of the Bott-Chern cohomology in terms of the Hodge numbers. We also give a generalization of this upper bound, with applications to symplectic cohomologies.

Tags: SIR2014-AnHyC


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