Uniruled varieties with split tangent bundle

2005/05/16 by Höring, Andreas
#14E30 #14J40 #32Q30 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0505327

Abstract

Beauville asked if a compact Kähler manifold with split 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.

Related

• Projective manifolds with splitting tangent bundles, I
• A characterization of uniruled compact Kähler manifolds
• Complex manifolds with split tangent bundle
• The structure of uniruled manifolds with split tangent bundle
• On varieties whose universal cover is a product of curves