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An improvement of a theorem of Van de Ven
Published/Copyright:
May 21, 2008
Abstract
In this paper we improve a classical result of Van de Ven which characterizes linear subspaces of 
as the only smooth closed subvarieties of for which the normal sequence splits (see [A. Van de Ven, A property of algebraic varieties in complex projective spaces. In: Colloque
Géom. Diff. Globale (Bruxelles, 1958), 151–152, Centre Belge Rech. Math., Louvain 1959. MR0116361 (22 #7149) Zbl 0092.14004]). Precisely we prove the following: Let X be a submanifold of of dimension ≥ 3, and Y ⊆ X a submanifold of X of dimension ≥ 2. Assume that Span(Y) = Span(X), where Span(X) is the smallest linear subspace of containing X. Then the exact sequence: 
splits if and only if X is a linear subspace of .
Received: 2006-10-30
Published Online: 2008-05-21
Published in Print: 2008-April
© de Gruyter 2008
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Articles in the same Issue
- A Kantor family admitting a normal F-factor constitutes a p-group
- Planar compact sets whose intersections are starshaped via orthogonally convex paths
- An improvement of a theorem of Van de Ven
- Quadratic modules of polynomials in two variables
- On arithmetic Zariski pairs in degree 6
- Ample vector bundles with zero loci of small Δ-genera
- Defect and Hodge numbers of hypersurfaces
- On rational maps from a general surface in to surfaces of general type
- Location of radial centres of convex bodies
