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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 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.

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