Strong openness of multiplier ideal sheaves and optimal $L^2$ extension

Abstract

In this note, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Kollár and Jonsson-Mustată implies the truth of twisted versions of the strong openness conjecture; our optimal $L^2$ extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.

11 pages,it has been accepted for publication in SCIENCE CHINA Mathematics

References in corpus (5)

• Effectiveness of Demailly's strong openness conjecture and related problems
• Optimal constant in an L^2 extension problem and a proof of a conjecture of Ohsawa
• Strong openness conjecture for plurisubharmonic functions
• Strong openness conjecture and related problems for plurisubharmonic functions
• Dynamic multiplier ideal sheaves and the construction of rational curves in Fano manifolds

Cited by in corpus (2)

• New characterizations of plurisubharmonic functions and positivity of direct image sheaves
• Twisted version of Strong openness property in $L^p$