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On a class of Kato manifolds

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we describe Kato manifolds, also known as manifolds with global spherical shell. We revisit Brunellaâ s proof of the fact that Katosurfaces admit locally conformally K\"ahler metrics, and we show that it holdsfor a large class of higher dimensional complex manifolds containing a globalspherical shell. On the other hand, we construct manifolds containing a globalspherical shell which admit no locally conformally K\"ahler metric. We then con-sider a specific class, which can be seen as a higher dimensional analogue of Inoue-Hirzebruch surfaces, and study several of their analytical properties. Inparticular, we give new examples, in any complex dimension $n\geq 3$, of com-pact non-exact locally conformally K\"ahler manifolds with algebraic dimension $n-2$, algebraic reduction bimeromorphic to $\C\Proj^{n-2}$ and admitting non-trivialholomorphic vector fields. These results are joint work with Nicolina Istrati(University of Tel Aviv) and Massimiliano Pontecorvo (Roma Tre University).

Mathematics; Differential geometry; Algebraic geometry

video/mp4

Author affiliation: Università Roma Tre

2020-04-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74195

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/