Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Congreso de la RSME 2017

Oeljeklaus-Toma manifolds and deformations (Variedades de Oeljeklaus-Toma y deformaciones)

Daniele Angella (Dipartimento di Matematica e Informatica "Ulisse Dini", Università di Firenze)

created by daniele on 05 Feb 2017

30 jan 2017 -- 17:00



Oeljeklaus-Toma manifolds are complex non-K\"ahler manifolds, which generalize the Inoue manifold. They have been introduced in \cite{oeljeklaus-toma} to answer a conjecture by Vaisman, and their construction is based on algebraic number theory \cite{ornea-vuletescu}.

In this talk, we present a joint work with Maurizio Parton and Victor Vuletescu \cite{angella-parton-vuletescu}. We prove that any holomorphic line bundle on an Oeljeklaus-Toma manifold of simple type (in particular, such manifolds have no divisor \cite{ornea-verbitsky, battisti-oeljeklaus}) is flat. We get that Oeljeklaus-Toma manifolds are rigid under deformations of the complex structure.

\bibitem{angella-parton-vuletescu}% Formato para artículo D. Angella, M. Parton, V. Vuletescu, Rigidity of Oeljeklaus-Toma manifolds, \texttt{arXiv:1610.04045}.

\bibitem{battisti-oeljeklaus} L. Battisti, K. Oeljeklaus, Holomorphic line bundles over domains in Cousin groups and the algebraic dimension of Oeljeklaus-Toma manifolds, \textit{Proc. Edinb. Math. Soc. (2)} \textbf{58} (2015), no.~2, 273--285.

\bibitem{oeljeklaus-toma}% Formato para artículo K. Oeljeklaus, M. Toma, Non-K\"ahler compact complex manifolds associated to number fields, \textit{Ann. Inst. Fourier (Grenoble)} \textbf{55} (2005), no.~1, 161--171.

\bibitem{ornea-verbitsky} L. Ornea, M. Verbitsky, Oeljeklaus-Toma manifolds admitting no complex subvarieties, \textit{Math. Res. Lett.} \textbf{18} (2011), no.~4, 747--754.

\bibitem{ornea-vuletescu} L. Ornea, V. Vuletescu, Oeljeklaus-Toma manifolds and locally conformally K\"ahler metrics. A state of the art, \textit{Stud. Univ. Babe\c{s}-Bolyai Math.} \textbf{58} (2013), no.~4, 459--468.


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