A proof of Demailly's strong openness conjecture

By Qi’an Guan, Xiangyu Zhou. 2015

225 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2b640f8483552fe910ebad873ddc088ef2f78c8d

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Citations in the corpus

A minimizing valuation is quasi-monomial (2019, background): “. On the other hand, it seems that our approach can not yield the stronger version [JM14, Conjecture C′′], which would imply the Strong Openness Conjecture. Nevertheless, the latter is also proved in [GZ15] (see also [Hie14,Lem17]). The proof of Theorem 1.1 depends on a combination of two sets of re”
A sharp effectiveness result of Demailly's strong openness conjecture (2017, background): “Recently, SOC was proved in [15] (see also [23, 18]).”
Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity (2017, background): “imate in (29) it follows that for each ℓ, Z Ω |F|2h−2ℓβn≤ B Z Ω ρAω n<+∞, hence |F|2e−2ℓlogh is integrable in Ω. From the resolution of Demailly’s strong openness conjecture [Dem] due to Guan-Zhou [GZh] (see also [Hiep] for an alternative proof) it follows that each |F|2h−2ℓ is in Lp(U,dV) for so”
A variational approach to the Yau–Tian–Donaldson conjecture (2015, methodology): “On the other hand, the assumption that θ is klt implies that e − 2 ψ locally in L p loc for some p > 1 [Bern15b, GZh15].”
The openness conjecture and complex Brunn-Minkowski inequalities (2014, methodology): “After that, simpler proofs and generalizations to the so called strong openness conjecture (see below), have been given by Guan-Zhou [13] and [14]; see also [16] and [19] for variants of the proof and simplifications.”
On the singularity type of full mass currents in big cohomology classes (2016, unknown): “mption that ν(Vθ,x) <γ. Now we argue the equality 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(”