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- Title
Hilbert Functions, Residual Intersections, and Residually S Ideals.
- Authors
Chardin, Marc; Eisenbud, David; Ulrich, Bernd
- Abstract
Let R be a homogeneous ring over an infinite field, I⊂ R a homogeneous ideal, and $$\mathfrak{a}$$ ⊂ I an ideal generated by s forms of degrees d,..., d so that codim( $$\mathfrak{a}$$ : I)≥ s. We give broad conditions for when the Hilbert function of R/ $$\mathfrak{a}$$ or of R/( $$\mathfrak{a}$$ : I) is determined by I and the degrees d,..., d. These conditions are expressed in terms of residual intersections of I, culminating in the notion of residually S ideals. We prove that the residually S property is implied by the vanishing of certain Ext modules and deduce that generic projections tend to produce ideals with this property.
- Publication
Compositio Mathematica, 2001, Vol 125, Issue 2, p193
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1023/A:1002442111114