Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds

摘要

Barth, Larsen, and others showed that complex submanifolds of complex projective space, CPN, of small codimension strongly resemble CPN both homotopically and cohomologically. These results are generalized to yield analogous results for complex subspaces of arbitrary homogeneous complex manifolds. One very special corollary that gives the flavor of the results is: