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Effective Nullstellensatz for arbitrary ideals

Effective Nullstellensatz for arbitrary ideals Let f i be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials g i such that ∑g i f i =1. The effective versions of this result bound the degrees of the g i in terms of the degrees of the f j . The aim of this paper is to generalize this to the case when the f i are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Effective Nullstellensatz for arbitrary ideals

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Publisher
Springer Journals
Copyright
Copyright © 1999 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970050009
Publisher site
See Article on Publisher Site

Abstract

Let f i be polynomials in n variables without a common zero. Hilbert’s Nullstellensatz says that there are polynomials g i such that ∑g i f i =1. The effective versions of this result bound the degrees of the g i in terms of the degrees of the f j . The aim of this paper is to generalize this to the case when the f i are replaced by arbitrary ideals. Applications to the Bézout theorem, to Łojasiewicz–type inequalities and to deformation theory are also discussed.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Sep 1, 1999

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