Effectiveness of Demailly’s strong openness conjecture and related problems

By Qi’an Guan, Xiangyu Zhou. Inventiones Mathematicae, 2014

101 citations recorded by the source corpus.

In this article, stimulated by the effectiveness in Berndtsson’s solution of the openness conjecture and continuing our solution of Demailly’s strong openness conjecture, we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result. We explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier, which is implicitly contained in Guan and Zhou (2014, arXiv:1401.7158). We also obtain optimal effectiveness of the conjectures of Demailly-Kollár and Jonsson-Mustată respectively.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/762711b2a63ef5aefb82c54307509a24b14e54f7

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In Applied Mathematics

1. Qi’an Guan
2. B. Berndtsson
3. Robert J. Berman
4. Xiangyu Zhou
5. Chi Li
6. Song Sun
7. László Lempert
8. Simon Donaldson

In Geometry and Topology

1. B. Berndtsson
2. Qi’an Guan
3. Robert J. Berman
4. Xiangyu Zhou
5. Chi Li
6. Junyan Cao
7. László Lempert
8. Song Sun

Citations in the corpus

• A sharp effectiveness result of Demailly's strong openness conjecture (2017, methodology): “1 in [16], implies the following Lemma (details see section 4.”
• The openness conjecture and complex Brunn-Minkowski inequalities (2014, methodology): “n introduction to how our ’complex Brunn-Minkowski inequalities’ can be applied. The method here also gives for free a bound on the exponents p, that can also be obtained in the setting of Guan-Zhou, [14], but with more work. In the last section we also give a very brief account of the strong openne”