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- Title
Q-Complete domains with corners in $${\mathbb{P}^n}$$ and extension of line bundles.
- Authors
Fornæss, John; Sibony, Nessim; Wold, Erlend
- Abstract
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.
- Subjects
FOLIATIONS (Mathematics); SUBMANIFOLDS; DIFFERENTIAL topology; MANIFOLDS (Mathematics); MATHEMATICS
- Publication
Mathematische Zeitschrift, 2013, Vol 273, Issue 1/2, p589
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-012-1021-0