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Bott-Chern cohomology of Vaisman manifolds

Nicolina Istrati (Philipps-Universität Marburg)
Wednesday 21 September 2022 14:00–15:00 Aud. D3 (1531-215)
Mathematics Seminar

Vaisman manifolds are complex manifolds which can be endowed with a special type of a Hermitian structure, namely a locally conformally Kähler metric with parallel Lee form. The geometry of Vaisman manifolds is closely related to Kählerian geometry, as these manifolds come endowed with a natural transversally Kähler foliation. However, Vaisman manifolds do not satisfy the dd^c-lemma, therefore it is interesting to study their Bott-Chern cohomology, which is then a refined invariant.

In this talk, I will explain how one can express this cohomology in terms of the basic cohomology with respect to the foliation, and in particular infer that the Bott-Chern numbers and the Dolbeault numbers determine each other. At the same time however, the numerical obstructions to the dd^c-lemma can be arbitrarily high.- This is based on joint work with Alexandra Otiman.

Organised by: Mathematics Group
Contact: Alexandra Otiman Revised: 14.09.2022