Foliations whose first Chern class is nef

Abstract

Let $\mathcal{F}$ be a foliation on a projective manifold $X$ with $-K_{\mathcal{F}}$ nef. Assume that either $\mathcal{F}$ is regular, or it has a compact leaf. We prove that there is a locally trivial fibration $f:X\to Y$ and a foliation $\mathcal{G}$ on $Y$ with $K_{\mathcal{G}}\equiv 0$ such that $\mathcal{F}=f^{-1}\mathcal{G}$.