On compact Kähler manifolds of nonnegative bisectional curvature, II

Abstract

This paper is a sequel to the preceding paper [HSW].This study of compact Kghler manifolds of nonnegative bisectional curvature was inspired by the recent solution of the Frankel conjecture by S. Mori ([M]) in a general algebraic setting, and subsequently by Siu and Yau ([SY]) in the special context of K/~hler geometry.With the ease of positive bisectional curvature out of the way, a general understanding of the case of nonnegative bisectional curvature is naturally the next order of business.For complex surfaces, the work of Howard and Smyth ([HS]) achieves a complete classification.In higher dimensions, the main conclusion of these two papers is that the study of compact Kahler manifolds of nonnegative bisectional curvature can be essentially reduced to the special case where simple connectivity and the isomorphism H2(M, Z)~Z are in addition assumed (the theorem of [HSW] and Theorem C below), and that with a mild positivity assumption these two desirable properties would follow in any ease (Theorem E below).We begin by listing the main results; their proofs will be given in subsequent sections,