In this short note we study foliations on surfaces with rationally connected leaves. Our main result is that on a surface there exists a polarisation such that the Harder-Narasimhan filtration of the tangent bundle with respect to this polarisation yields the maximal rationally connected quotient of the surface.
Cite this article
Sebastian Neumann, Rationally connected foliations on surfaces. Doc. Math. 14 (2009), pp. 157–165DOI 10.4171/DM/268