Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 49, Number 3 (2012), 833-852.
A transcendental approach to Kollár's injectivity theorem
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.
Osaka J. Math. Volume 49, Number 3 (2012), 833-852.
First available in Project Euclid: 15 October 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ojm/1350306598.