Strong openness of multiplier ideal sheaves and optimal $L^{2}$ extension
Complex Variables
2017-05-24 v2 Algebraic Geometry
Differential Geometry
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-Koll\'{a}r and Jonsson-Mustat\u{a} implies the truth of twisted versions of the strong openness conjecture; our optimal extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.
Keywords
Cite
@article{arxiv.1703.08387,
title = {Strong openness of multiplier ideal sheaves and optimal $L^{2}$ extension},
author = {Qi'an Guan and Xiangyu Zhou},
journal= {arXiv preprint arXiv:1703.08387},
year = {2017}
}
Comments
11 pages,it has been accepted for publication in SCIENCE CHINA Mathematics