The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type (1, 0). In a coordinate chart z = (z_1, ..., z_n), the bundle is spanned by the local bundle sections d/dz_k. The antiholomorphic sections are spanned by d/dz^__k, of type (0, 1), where z^_ denotes the complex conjugate.

complex structure | Hermitian metric | holomorphic line bundle | holomorphic vector bundle | tangent bundle