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• 作者：John Erik Forn?ss (1) (2)
  Nessim Sibony (3)
  Erlend F. Wold (4)
  
• 关键词：Line bundles ; Foliations ; q ; Convex ; Primary 32D15 ; Secondary 32F10
• 刊名：Mathematische Zeitschrift
• 出版年：2013
• 出版时间：2 - February 2013
• 年：2013
• 卷：273
• 期：1
• 页码：589-604
• 全文大小：257KB
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  15. Siu Y.-T.: ${\overline{\partial}}$ ?regularity for weakly pseudoconvex domains in compact Hermitian symmetric spaces with respect to invariant metrics. Ann. Math. (2) 156(2), 595-21 (2002) CrossRef
  
• 作者单位：John Erik Forn?ss (1) (2)
  Nessim Sibony (3)
  Erlend F. Wold (4)
  
  1. NTNU, 7491, Trondheim, Norway
  2. Mathematical Sciences Center, Tsinghua University, Beijing, China
  3. Université Paris-Sud, Mathematique, 91405, Orsay Cedex, France
  4. Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316, Oslo, Norway
  
• ISSN：1432-1823

文摘

We show that if a compact set X in ${\mathbb P^n}$ is laminated by holomorphic submanifolds of dimension q, then ${\mathbb P^n{\setminus}X}$ is (q?+?1)-complete with corners. Consider a manifold U, q-complete with corners. Let ${\mathcal N}$ be a holomorphic line bundle in the complement of a compact in U. We study when ${\mathcal N}$ extends as a holomorphic line bundle in U. We give applications to the non existence of some Levi-flat foliations in open sets in ${\mathbb P^n}$ . The results apply in particular when U is a Stein manifold of dimension n??3, then every holomorphic line bundle in the complement of a compact extends holomorphically to U.