Effective Nullstellensatz for arbitrary ideals

Abstract

Abstract. Let fi be polynomials in n variables without a common zero. Hilbert's Nullstellensatz says that there are polynomials gi such that ~gifi=1. The effective versions of this result bound the degrees of the gi in terms of the degrees of the fj. The aim of this paper is to generalize this to the case when the fi are replaced by arbitrary ideals. Applications to the Bézout theorem, to Lojasiewicz-type inequalities and to deformation theory are also discussed.