For algebraic number fields with real and complex embeddings and “admissible” subgroups of the multiplicative group of integer units of we construct and investigate certain -dimensional compact complex manifolds . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when . In particular we disprove a conjecture of I. Vaisman.
Etant donnés des corps de nombres avec plongements réels et plongements complexes, et des sous groupes “admissibles” du groupe multiplicatif des entiers inversibles de , nous construisons et étudions certaines variétés complexes compactes . Entre autres, nous montrons que ces variétés ne sont pas kähleriennes, mais admettent des métriques localement conformément kähleriennes lorsque . En particulier, nous donnons un contre-exemple à une conjecture de I. Vaisman.
Keywords: Compact complex manifolds, algebraic number fields, algebraic units, locally conformally Kähler metrics
Mot clés : variété complexe compacte, corps de nombres, métrique localement conformément Kählerienne.
@article{AIF_2005__55_1_161_0, author = {Oeljeklaus, Karl and Toma, Matei}, title = {Non-K\"ahler compact complex manifolds associated to number fields}, journal = {Annales de l'Institut Fourier}, pages = {161--171}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {1}, year = {2005}, doi = {10.5802/aif.2093}, mrnumber = {2141693}, zbl = {1071.32017}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2093/} }
TY - JOUR AU - Oeljeklaus, Karl AU - Toma, Matei TI - Non-Kähler compact complex manifolds associated to number fields JO - Annales de l'Institut Fourier PY - 2005 SP - 161 EP - 171 VL - 55 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2093/ DO - 10.5802/aif.2093 LA - en ID - AIF_2005__55_1_161_0 ER -
%0 Journal Article %A Oeljeklaus, Karl %A Toma, Matei %T Non-Kähler compact complex manifolds associated to number fields %J Annales de l'Institut Fourier %D 2005 %P 161-171 %V 55 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2093/ %R 10.5802/aif.2093 %G en %F AIF_2005__55_1_161_0
Oeljeklaus, Karl; Toma, Matei. Non-Kähler compact complex manifolds associated to number fields. Annales de l'Institut Fourier, Volume 55 (2005) no. 1, pp. 161-171. doi : 10.5802/aif.2093. http://archive.numdam.org/articles/10.5802/aif.2093/
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