Comptes Rendus
no. 4
Complex analysis/Analytic geometry
Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem

Presented by: Jean-Pierre Demailly

Qi'an Guan1; Xiangyu Zhou2
1 School of Mathematical Sciences, and Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
2 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China
Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 415-419.

In this note, we describe a relation between Lelong numbers and complex singularity exponents. As an application, we obtain a new proof of Siu's semicontinuity theorem for Lelong numbers.

Dans cette note, nous décrivons une relation entre les nombres de Lelong et les exposants de singularités complexes. Comme application, nous obtenons une nouvelle preuve du théorème de semi-continuité de Siu pour les nombres de Lelong.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.03.006

Qi'an Guan 1; Xiangyu Zhou 2

1 School of Mathematical Sciences, and Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
2 Institute of Mathematics, AMSS, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, China 
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Qi'an Guan; Xiangyu Zhou. Lelong numbers, complex singularity exponents, and Siu's semicontinuity theorem. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 415-419. doi : 10.1016/j.crma.2017.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.03.006/

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☆ The authors were partially supported by NSFC-11431013. The second author would like to thank NTNU for offering him Onsager Professorship. The first author was partially supported by NSFC-11522101.

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