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arXiv · 1507.07108

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

Daniele Angella·Nicoletta Tardini
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Abstract

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.

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Daniele Angella, Nicoletta Tardini. 2015-07-25. Quantitative and qualitative cohomological properties for non-K\"ahler manifolds. https://doi.org/10.1090/proc/13209

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