A. Pereira do Vale & M. R. Pinto (ed.),
Proceedings of the 1st International Meeting on Geometry and Topology.
Proceedings of the conference held in Braga, September 11-13, 1997.
Universidade do Minho, Portugal

The holomorphic fiber bundle structure of some compact complex nilmanifolds

Luis A. Cordero, Marisa Fernandez, Alfred Gray and Luis Ugarte

Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad de Santiago de Compostela, 15705 Santiago de Compostela, Spain cordero@zmat.usc.es

Departamento de Matematicas, Facultad de Ciencias, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain mtpferol@lg.ehu.es

Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA gray@bianchi.umd.edu

Departamento de Geometria y Topologia, Facultad de Ciencias, Universidad de Zaragoza, Campus Pl. San Francisco, 50009 Zaragoza, Spain ugarte@posta.unizar.es

Abstract: Strongly non-nilpotent complex structures on compact complex nilmanifolds $\nilm$ are defined and characterized. As an application, a compact complex nilmanifold $\nilm$ with a non-nilpotent complex structure which is not strongly non-nilpotent is described as the total space at the top in a tower of holomorphic principal torus bundles. This description extends the one given by L.A. Cordero, M. Fernandez, A. Gray and L. Ugarte [Compact nilmanifolds with nilpotent complex structure: Dolbeault cohomology, Preprint 1997]. The problem of computing the Dolbeault cohomology of $\nilm$ is also discussed.

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