Effectiveness of Demailly's strong openness conjecture and related problems

• 成果类型: Article
• 署名作者: Guan, Qi'an; Zhou, Xiangyu
• 署名单位: Peking University; Peking University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0575-3
• 发表日期: 2015
• 页码: 635-676
• 关键词: multiplier ideal sheaves; kahler-einstein metrics; l-2 extension theorem; ohsawa-takegoshi; holomorphic-functions; vanishing theorem; VALUATIONS; complex; acc

摘要

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-Kollar and Jonsson-Mustat respectively.