Hilbert Functions, Residual Intersections, and Residually S2 Ideals |
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Authors: | Marc Chardin David Eisenbud Bernd Ulrich |
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Affiliation: | (1) Institut de Mathématiques, CNRS & Université Paris 6, 4, place Jussieu, F–75252 Paris Cedex 05, France;(2) Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, CA, 94720, U.S.A.;(3) Department of Mathematics, Michigan State University, East Lansing, MI, 48824, U.S.A. |
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Abstract: | Let R be a homogeneous ring over an infinite field, I R a homogeneous ideal, and ![$$mathfrak{a}$$](/content/g82q4321t2230l8r/10599_2004_Article_256510_TeX2GIFIE1.gif) I an ideal generated by s forms of degrees d1,...,ds so that codim( :I) s. We give broad conditions for when the Hilbert function of R/ or of R/( :I) is determined by 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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Keywords: | Hilbert function Hilbert polynomial residual intersection residually S2 parsimonious thrifty |
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