Osaka Journal of Mathematics

A transcendental approach to Kollár's injectivity theorem

Osamu Fujino

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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.

Article information

Osaka J. Math. Volume 49, Number 3 (2012), 833-852.

First available in Project Euclid: 15 October 2012

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Zentralblatt MATH identifier

Primary: 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
Secondary: 32W05: $\overline\partial$ and $\overline\partial$-Neumann operators


Fujino, Osamu. A transcendental approach to Kollár's injectivity theorem. Osaka J. Math. 49 (2012), no. 3, 833--852.

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