Absolutely fe-convex domains and holomorphic foliations on homogeneous manifolds

摘要

We consider a holomorphic foliation T of codimension k ≥ 1 on a homogeneous compact Kahler manifold X of dimension n > k. Assuming that the singular set Sing(F) of F is contained in an absolutely k-convex domain U ⊂ X, we prove that the determinant of normal bundle det(N_F) of F cannot be an ample line bundle, provided [n/k] ≥ 2k + 3. Here [n/k] denotes the largest integer < n/k.