Bochner-Hartogs type extension theorem for roots and logarithms of holomorphic line bundles

被引:0
作者
S. Ivashkovich
机构
[1] Université Lille-1,UFR de Mathématiques
[2] National Academy of Sciences of Ukraine,Pidstryhach Institute for Applied Problems of Mechanics and Mathematics
来源
Proceedings of the Steklov Institute of Mathematics | 2012年 / 279卷
关键词
Line Bundle; STEKLOV Institute; Complex Manifold; Plurisubharmonic Function; Holomorphic Line Bundle;
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学科分类号
摘要
We prove an extension theorem for roots and logarithms of holomorphic line bundles across strictly pseudoconcave boundaries: they extend in all cases except one, when the dimension and Morse index of a critical point is 2. In that case we give an explicit description of obstructions to the extension.
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页码:257 / 275
页数:18
相关论文
共 15 条
[1]  
Bochner S.(1938)A Theorem on Analytic Continuation of Functions in Several Variables Ann. Math., Ser. 2 39 14-19
[2]  
Dethloff G.-E.(1990)A New Proof of a Theorem of Grauert and Remmert by Math. Ann. 286 129-142
[3]  
Forstnerič F.(2003)-Methods J. Geom. Anal. 13 77-94
[4]  
Frenkel J.(1957)Stein Domains in Complex Surfaces Bull. Soc. Math. France 85 135-220
[5]  
Grauert H.(1958)Cohomologie non abélienne et espaces fibrés Math. Ann. 136 245-318
[6]  
Remmert R.(1981)Komplexe Räume Izv. Akad. Nauk SSSR, Ser. Mat. 45 896-904
[7]  
Ivashkovich S. M.(1992)Envelopes of Holomorphy of Some Tube Sets in Invent. Math. 109 47-54
[8]  
Ivashkovich S. M.(1998) and the Monodromy Theorem Mat. Zametki 63 599-606
[9]  
Nemirovskii S. Yu.(1977)The Hartogs-Type Extension Theorem for Meromorphic Maps into Compact Kähler Manifolds Bull. Soc. Math. France 105 191-223
[10]  
Norguet F.(2000)Holomorphic Functions and Embedded Real Surfaces Nagoya Math. J. 158 95-98