Rational curves on compact Kähler manifolds

Abstract

Mori’s theorem yields the existence of rational curves on projective manifolds such that the canonical bundle is not nef. In this paper we study compact Kähler manifolds such that the canonical bundle is pseudoeffective, but not nef. We present an inductive argument for the existence of rational curves that uses neither deformation theory nor reduction to positive characteristic. The main tool for this inductive strategy is a weak subadjunction formula for log-canonical centres associated to certain big cohomology classes.