Absolutely k-convex domains and holomorphic foliations on homogeneous manifolds

作者：Correa Mauricio Jr^*; Fernandez Perez Arturo

来源：Journal of the Mathematical Society of Japan, 2017, 69(3): 1235-1246.

DOI：10.2969/jmsj/06931235

• holomorphic foliations
• absolutely q-convex spaces

We consider a holomorphic foliation,F of codimension k >= 1 on a homogeneous compact Kahler manifold X of dimension n > k. Assuming that the singular set Sing(F) of is contained in an absolutely k-convex domain U subset of 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.

• 出版日期2017-7