Uniruled varieties with split tangent bundle

Beauville asked if a compact Kaehler manifold with splitting tangent bundle has a universal covering that is a product of manifolds. We use Mori theory and elementary results about holomorphic foliations to study this problem for projective uniruled varieties. In particular we obtain an affirmative...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2007-07, Vol.256 (3), p.465-479
Main Author: Höring, Andreas
Format: Article
Language:English
Subjects:
Algebraic Geometry
Mathematics
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Summary:Beauville asked if a compact Kaehler manifold with splitting tangent bundle has a universal covering that is a product of manifolds. We use Mori theory and elementary results about holomorphic foliations to study this problem for projective uniruled varieties. In particular we obtain an affirmative answer for rationally connected varieties in any dimension and uniruled varieties in dimension 4.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-006-0072-5