  Let \omega be a Pfaff system of differential forms on a projective space. Let
S be its singular locus, and Y a solution of \omega=0. We prove Y\cap S is of
codimension at most 1 in Y, just as Jouanolou suspected; he proved this result
assuming \omega is completely integrable, and asked if the integrability is, in
fact, needed. Furthermore, we prove a lower bound on the Castelnuovo--Mumford
regularity of Y\cap S. As in two related articles, we derive upper bounds on
numerical invariants of Y, thus contributing to the solution of the Poincare
problem. We work with Pfaff fields not necessarily induced by Pfaff systems,
with ambient spaces more general than projective spaces, and usually in
arbitrary characteristic.
