Eberhard Obeljeklaus
Meromorphic function fields of Albanese bundles
The paper is published: Rostocker Mathematische Kolloquium, Rostock. Math. Kolloq. 47,3-22 (1994)

MSC:

32L05 Holomorphic fiber bundles and generalizations

32M05 Complex Lie groups, automorphism groups of complex spaces, See also {22E10}

Abstract: Let X be a (connected) compact complex manifold ad Aut X the complex
Lie group of biholomorphic transformations of X. The Albanese torus A(X)
of X is a bimeromorphic invariant of X, and the holomorphic Albanese
map \alpha:X\to A(X) often yields important information about the
holomorphic or meromorphic structure of X. For example, if X is
kählerian and if c_1(X)\ge 0 or Aut X has an open orbit on X,
then \alpha:X\to A(X) is a holomorphic fiber bundle and much is known
about the topological and holomorphic structure of X. In particular,
if Aut X operates transitively on X, then X splits biholomorphically
into a product A(X)\time F with projective rational manifold F.
Notes: Abstract contains the first 10 lines of text of the paper.