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Effective Nullstellensatz for arbitrary ideals

János Kollár (1999)

Journal of the European Mathematical Society

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 inequalities and to deformation theory are also discussed.

Ends of varieties

H. Alexander (1992)

Bulletin de la Société Mathématique de France

Equivalence of analytic and rational functions

J. Bochnak, M. Buchner, W. Kucharz (1997)

Annales Polonici Mathematici

We give a criterion for a real-analytic function defined on a compact nonsingular real algebraic set to be analytically equivalent to a rational function.

Errata to "Multiplicity and the Łojasiewicz exponent" (Ann. Polon. Math. 73 (2000), 257-267)

Stanisław Spodzieja (2015)