Mathematical Research Letters

Volume 24 (2017)

Number 6

A generalized Siu’s lemma

Pages: 1897 – 1913

DOI: https://dx.doi.org/10.4310/MRL.2017.v24.n6.a16

Authors

Xiangyu Zhou (Institute of Mathematics, AMSS and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China)

Langfeng Zhu (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Abstract

In this paper, we obtain a generalization of Siu’s lemma by using the openness property of multiplier ideal sheaves as a tool. Meanwhile, we give another proof of the openness property of multiplier ideal sheaves proved by Berndtsson.

Full Text (PDF format)

Xiangyu Zhou was partially supported by the National Natural Science Foundation of China (No. 11688101 and No. 11431013). Langfeng Zhu was partially supported by the National Natural Science Foundation of China (No. 11201347 and No. 11671306) and the China Scholarship Council. Langfeng Zhu would like to thank Professor Xiaojun Huang and his student Hanlong Fang for their hospitality during his visit at Rutgers University.

Received 8 February 2017

Accepted 8 October 2017

Published 29 January 2018