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Hilbert Functions and Generic Forms

Published online by Cambridge University Press:  04 December 2007

JÜRGEN HERZOG  and
DORIN POPESCU
JÜRGEN HERZOG
Affiliation:
FB 6 Mathematik und Informatik, Universitä – GHS – Essen, Postfach 103764, 45117 Essen, Germany; e-mail: mat300@uni-essen.de
DORIN POPESCU
Affiliation:
Institute of Mathematics, University of Bucharest, P.O. Box 1-764, Bucharest 70700, Romania; e-mail: dpopescu@roimar.imar.ro, or: dorin@stoilow.imar.ro
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Abstract

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Let A be a homogeneous K-algebra where K is a field of characteristic 0, and h ∈ A a generic form. We bound the Hilbert function H(A/(h),-) in terms of H(A,-) which extends the bound given by M. Green for generic linear forms. We apply this to some conjectures from Higher Castelnuovo Theory and Cayley-Bacharach Theory.

Keywords

Hilbert functionsGreen and Gotzmann theoremsCayley-BacharachHigher Castelnuovo Theory.
Type
Research Article
Information
Compositio Mathematica , Volume 113 , Issue 1 , August 1998 , pp. 1 - 22
Copyright
© 1998 Kluwer Academic Publishers