26 feb 2017 -- 09:30
Aula Bianchi, SNS, Pisa
Abstract.
``OT manifolds'' have been introduced by K. Oeljeklaus and M. Toma in 2005 to answer a conjecture by Vaisman in locally conformal geometry. They are constructed using techniques of algebraic number theory and generalize the Inoue-Bombieri surface to higher dimensions.
We present a joint work with Maurizio Parton and Victor Vuletescu (arXiv:1610.04045). We prove that any line bundle on OT manifolds ``of simple-type'' is flat. Similar arguments, exploiting both algebraic and analytic techniques, allow to prove a vanishing result for cohomology. As a consequence, we get rigidity of OT manifolds under deformations of the complex structure.