Uniruled varieties with splitting tangent bundle

Details Uniruled varieties with splitting tangent bundle Uniruled varieties with splitting tangent bundle

2005-05-16

arxiv.org/abs/math/0505327v2

Mathematics

Algebraic Geometry

25 pages, reasons for resubmission: corrected typo in theorem 1.6, improved exposition

Scientific paper

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.

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