Algebraic degeneracy theorem on complete Kähler manifolds

Abstract

In this paper, we develop an algebraic degeneracy theorem for meromorphic mappings from Kähler manifolds into complex projective manifolds provided that the dimension of target manifolds is not greater than that of source manifolds. With some curvature or growth conditions imposed, we show that any meromorphic mapping must be algebraically degenerate if it satisfies a defect relation.