Cohomological properties of non-Kahler manifolds

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• Daniele Angella (Universita degli Studi di Firenze)
• Wednesday 25 May 2016, 11:00-12:00
• CMS MR13.

If you have a question about this talk, please contact Dr. J Ross.

Besides the Dolbeault cohomology, the Bott-Chern cohomology provides a further invariant in the geometry of complex non-Kahler manifolds. It may encode, in a sense, more informations on the complex and geometric structures, and it arises as a natural tool in investigating special Hermitian metrics.

We study cohomologies on complex manifolds, focusing on both their algebraic structure, and on how they are related each other. In particular, we provide inequalities à la Fr\”olicher to compare the dimensions of the Bott-Chern cohomology and the Hodge and Betti numbers. We use such an inequality to characterize the cohomological decomposition property known as dbar-Lemma property, and to provide in fact a degree of non-Kahlerness for compact complex surfaces. Moreover, we try an attempt to understand a notion of formality in the context of Bott-Chern cohomology.

This talk is part of the Algebraic Geometry Seminar series.

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