  In this article we establish bounds for the Castelnuovo-Mumford regularity of
projective schemes in terms of the degrees of their defining equations. The
main new ingredient in our proof is to show that generic residual intersections
of complete intersection rational singularities again have rational
singularities. When applied to the theory of residual intersections this circle
of ideas also sheds new light on some known classes of free resolutions of
residual ideals.
