Stability of Holomorphic Foliations with Split Tangent Sheaf

Details Stability of Holomorphic Foliations with Split Tangent Sheaf Stability of Holomorphic Foliations with Split Tangent Sheaf

2005-11-02

arxiv.org/abs/math/0511060v3

American Journal of Mathematics Vol. 130, No. 2, pp. 413-439, 2008.

Mathematics

Complex Variables

Final version, to appear in American Journal of Math

Scientific paper

10.1353/ajm.2008.0011

We show that the set of singular holomorphic foliations of the projective spaces with split tangent sheaf and with good singular set is open in the space of holomorphic foliations. As applications we present a generalization of a result by Camacho-Lins Neto about linear pull-back foliations, we give a criterium for the rigidity of $\mathcal L$-foliations of codimension $k \ge 2$ and prove a conjecture by Cerveau-Deserti about the rigidity of a codimension one $\mathcal L$-foliation of $\mathbb P^4$. These results allow us to exhibit some previously unknown irreducible components of the spaces of singular holomorphic foliations.

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