A transcendental approach to Kollár's injectivity theorem

Abstract

We treat Kollár's injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Kollár type cohomology injectivity theorems. Our main theorem is formulated for a compact Kähler manifold, but the proof uses the space of harmonic forms on a Zariski open set with a suitable complete Kähler metric. We need neither covering tricks, desingularizations, nor Leray's spectral sequence.

22 pages; a minor revision of the preprint circulated in January 2006, v2: minor modifications, v3: final version, to appear in Osaka J. Math