Modules of Square Integrable Holomorphic Germs

By László Lempert. 2014

53 citations recorded by the source corpus.

This paper was inspired by Guan and Zhou’s recent proof of the socalled strong openness conjecture for plurisubharmonic functions. We give a proof shorter than theirs and extend the result to possibly singular Hermitian metrics on vector bundles.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c93dc2bcf8d11d61866f3ccce0587d6b8acb38bd

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A sharp effectiveness result of Demailly's strong openness conjecture (2017, result): “of SOC so-called the openness conjecture (OC for short) was proved by Berndtsson [2] and the two-dimensional case of OC was proved by Favre-Jonsson [10, 9]. Recently, SOC was proved in [15] (see also [23, 18]). After that, stimulated by the eﬀectiveness result in Berndtsson’s solution of the opennes”
On the singularity type of full mass currents in big cohomology classes (2016, methodology): “lity of multiplier ideal sheafs in (i). This will be an application of Theorem 1.2 and the resolution of the strong openess conjecture of Guan and Zhou [GuZh], in the speciﬁc form provided by Lempert [Lemp]. Indeed, from Theorem 1.2 it follows that Pθ(ϕ+c,Vθ)(x) ր Vθ(x) as c→ ∞, for a.e. x∈ X. (25) ”
A proof of Demailly's strong openness conjecture (2015, methodology): “We would like to thank the referee for kindly pointing out that as observed by Lempert in [23], Lemma 2.”
A general extension theorem for cohomology classes on non reduced analytic subspaces (2017, background): “unded above, we infer that property (d) holds. Finally we check the last conclusion of property (c) by proving the following lemma, which can be obtained from the strong openness theorem (see [GZ15], [Lem14], [Hie14]) and property (e). Lemma3.3. For a quasi-psh function ϕ, we have I(he−ϕ) = I(hεe−ϕ)”