Effective Nullstellensatz for arbitrary ideals

  • János Kollár

    Fine Hall / Princeton University, USA


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

Cite this article

János Kollár, Effective Nullstellensatz for arbitrary ideals. J. Eur. Math. Soc. 1 (1999), no. 3, pp. 313–337

DOI 10.1007/S100970050009