An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities

By Shin-ichi Matsumura. 2013

67 citations recorded by the source corpus.

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel type vanishing theorem. For the proof, we study the asymptotic behavior of the harmonic forms with respect to a family of regularized metrics, and give a method to obtain L2-estimates of solutions of the dbar-equation by using the de Rham-Weil isomorphism between the dbar-cohomology and the check{C}ech cohomology.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6642c0e12290c79a80edc08c97dd5b1ba1c1aa48

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In Applied Mathematics

1. Qi’an Guan
2. Xiangyu Zhou
3. B. Berndtsson

In Geometry and Topology

1. Qi’an Guan
2. Xiangyu Zhou
3. B. Berndtsson
4. Junyan Cao

Citations in the corpus

• A proof of Demailly's strong openness conjecture (2015, result): “A similar result when X is a projective manifold can be found in [24].”
• Effectiveness of Demailly’s strong openness conjecture and related problems (2014, background): “Recall that the multiplier ideal sheaf I(φ) is the sheaf of germs of holomorphic functions f such that | f |2e−φ is locally integrable (see [33], see also [7,27,29,32,41,42], etc.”