Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Aeppli Cohomology and Gauduchon Metrics

Riccardo Piovani

created by daniele on 12 Sep 2019
modified on 05 Nov 2019

14 nov 2019 -- 14:00

Aula Tricerri, DiMaI, Firenze

Abstract.

Given a Gauduchon metric g on a compact complex manifold M of complex dimension n, one may study whether the Aeppli cohomology class represented by the (n-1) power of the fundamental form of the metric vanishes or not. In the seminar we will discuss about some new results about the topic, contained in a joint preprint by Adriano Tomassini and the speaker. In particular, we will show that if the above mentioned Aeppli cohomology class vanishes, then the Bott-Chern cohomology group of bigrade (1,0) vanishes also. Furthermore, the same phenomenon will be proven to hold in a more general setting, considering a complete Hermitian metric g on M (non-necessarily compact).

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