**MSC:**- 32L05 Holomorphic fiber bundles and generalizations
- 32M05 Complex Lie groups, automorphism groups of complex spaces, See also {22E10}

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.