Non-Kähler compact complex manifolds associated to number fields

Oeljeklaus, Karl, and Toma, Matei. "Non-Kähler compact complex manifolds associated to number fields." Annales de l’institut Fourier 55.1 (2005): 161-171. <http://eudml.org/doc/116182>.

@article{Oeljeklaus2005,
abstract = {For algebraic number fields $K$ with $s&gt;0$ real and $2t&gt;0$ 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.},
affiliation = {Université d'Aix-Marseille I, LATP-UMR(CNRS) 6632, CMI, 39, rue Joliot-Curie, 13453 Marseille Cedex 13 (France), Institute of Mathematics of the Romanian Academy, Bucharest, 014700 (Roumanie)},
author = {Oeljeklaus, Karl, Toma, Matei},
journal = {Annales de l’institut Fourier},
keywords = {Compact complex manifolds; algebraic number fields; algebraic units; locally conformally Kähler metrics; compact complex manifold; algebraic number field; locally conformal Kähler metric},
language = {eng},
number = {1},
pages = {161-171},
publisher = {Association des Annales de l'Institut Fourier},
title = {Non-Kähler compact complex manifolds associated to number fields},
url = {http://eudml.org/doc/116182},
volume = {55},
year = {2005},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 1
SP - 161
EP - 171
AB - For algebraic number fields $K$ with $s&gt;0$ real and $2t&gt;0$ 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.
LA - eng
KW - Compact complex manifolds; algebraic number fields; algebraic units; locally conformally Kähler metrics; compact complex manifold; algebraic number field; locally conformal Kähler metric
UR - http://eudml.org/doc/116182
ER -