A Poincaré type inequality for one-dimensional multiprojective foliations.

We study one-dimensional holomorphic foliations on products of complex projective spaces and present results giving the number of singularities, counting multiplicities, of a generic foliation, a criterion for a foliation to be Riccati and a Poincaré type inequality, relating degrees of foliations to degrees of hypersurfaces which are invariant by them. [ABSTRACT FROM AUTHOR]