Abstract
Let R be a homogeneous ring over an in¢nite ¢eld, I R a homogeneous ideal, and a I an ideal generated by s forms of degrees d1; ... ;ds so that codimOa : IUXs.We give broad conditionsfor whenthe Hilbertfunction ofR=aorofR=Oa : IUis determinedby I and the degrees d1; ... ;ds.These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S2 ideals. We prove that the residually S2 property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property.
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