Non-Kähler compact complex manifolds associated to number fields
Annales de l'Institut Fourier, Volume 55 (2005) no. 1, p. 161-171
For algebraic number fields K with s>0 real and 2t>0 complex embeddings and “admissible” subgroups U of the multiplicative group of integer units of K we construct and investigate certain (s+t)-dimensional compact complex manifolds X(K,U). We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when t=1. In particular we disprove a conjecture of I. Vaisman.
Etant donnés des corps de nombres K avec s>0 plongements réels et 2t>0 plongements complexes, et des sous groupes “admissibles” U du groupe multiplicatif des entiers inversibles de K, nous construisons et étudions certaines variétés complexes compactes X(K,U). Entre autres, nous montrons que ces variétés ne sont pas kähleriennes, mais admettent des métriques localement conformément kähleriennes lorsque t=1. En particulier, nous donnons un contre-exemple à une conjecture de I. Vaisman.
DOI : https://doi.org/10.5802/aif.2093
Classification:  32J18,  32M17
Keywords: Compact complex manifolds, algebraic number fields, algebraic units, locally conformally Kähler metrics
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {1},
     year = {2005},
     pages = {161-171},
     doi = {10.5802/aif.2093},
     mrnumber = {2141693},
     zbl = {1071.32017},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2005__55_1_161_0}
}
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. https://aif.centre-mersenne.org/item/AIF_2005__55_1_161_0/

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