5 oct 2022 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
A complex manifold $M$ of $dim_C M = n$ has holomorphically trivial canonical bundle if and only if $M$ admits a closed nowhere vanishing $(n, 0)$-form. Recently compact complex manifolds with this property have been intensively studied. For instance, every nilmanifold equipped with an invariant complex structure has trivial canonical bundle (Cavalcanti- Gualtieri, Barberis-Dotti-Verbitsky). This talk is divided in two parts: first we will give a characterization of Lie algebras equipped with a complex structure $J$ admitting a closed $(n, 0)$-form and see some consequences and applications to hypercomplex geometry. Next we will focus on providing some examples of solvmanifolds $\Gamma\backslash G$ admitting a non-invariant closed $(n, 0)$-form $\sigma$, that is, $\sigma$ is not left-invariant. Finally, we will construct examples of compact complex manifolds with holomorphically trivial canonical bundle using Morimoto’s construction starting with two normal almost contact manifolds. This is joint work in progress with Adrian Andrada.