Complex Analytic Geometry of Complex Parallelizable Manifolds

Memoirs Soc. Math. France 72/73. 1998

Jörg Winkelmann

(ISBN: 2-85629-070-1)


Quotients of Complex Lie groups by discrete subgroups are studied as complex manifolds. In particular, holo- and meromorphic functions, subvarieties, deformations, cohomology and vector bundles are investigated. This book is an expanded and revised version of my Habilitationsschrift . Many results have been generalized from the special case of cocompact lattices to arbitrary lattices. Furthermore, some preparational and background material has been added. A survey on the results is given in an article in the proceedings of Geometric Complex Analysis.

Corrections, Misprints, Remarks and Annotations

On p.38, Remark 3.6.4 states without proof that a lattice in a nilpotent locally compact topological group is necessarily cocompact. I have been asked about the proof, which is available here.

The remark on K3-surfaces on page 129 needs some clarification .

Related later articles

On Complex Analytic Compactifications of Complex Parallelizable Manifolds (2000)
On Elliptic Curves in SL2(C)/Gamma, Schanuel's conjecture and geodesic lengths. (2002)
On Varieties with trivial logarithmic tangent bundle.
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