Effective Nullstellensatz for Arbitrary Ideals

János Kollár

paper

Effective Nullstellensatz for Arbitrary Ideals

arXiv:math/9805091

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 $\sum g_{i} f_{i} = 1$ . 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 inequialities and to deformation theory are also discussed.

LATEX2e, 25 pages