  A Pfaff field on a projective space is a map from the sheaf of differential
s-forms, for a certain s, to an invertible sheaf. The interesting ones are
those arising from a Pfaff system, as they give rise to a distribution away
from their singular locus. A subscheme of the projective space is said to be
invariant under the Pfaff field, if the latter induces a Pfaff field on the
subscheme. We give bounds for the Castelnuovo-Mumford regularity of invariant
complete intersection subschemes (more generally, arithmetically Cohen-Macaulay
subschemes) of dimension s, depending on how singular these schemes are, thus
bounding the degrees of the hypersurfaces that cut them out.
