KolloquiumGRK On the Bott-Chern Cohomology of Vaisman manifolds |  |
Speaker:Nicolina Istrati, Philipps-Universität Marburg
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerZoom: https://uni-goettingen.zoom.us/j/91336854872 Live Stream: http://streaming.math.uni-goettingen.de/Gras Geo Map
Organizer:Fakultät für Mathematik und Informatik
Details:
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. Typical examples are given by holomorphic principal torus bundles over a projective manifold with prescribed characteristic class. More generally, the geometry of Vaisman manifolds is closely related to Kählerian geometry, as these manifolds always 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.
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Type:Colloquium
Language:English
Category:Research
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Direct link to event:https://events.goettingen-campus.de/event?eventId=28322
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