Geodesic
Effective Nullstellensatz for arbitrary ideals
Journal of the European Mathematical Society, Tome 1 (1999) no. 3, pp. 313-337

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Let fi​ be polynomials in n variables without a common zero. Hilbert's Nullstellensatz says that there are polynomials gi​ such that ∑gi​fi​=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 Łojasiewicz-type inequalities and to deformation theory are also discussed.
DOI : 10.1007/s100970050009
Classification : 12-XX, 11-XX, 14-XX, 32-XX 
János Kollár. Effective Nullstellensatz for arbitrary ideals. Journal of the European Mathematical Society, Tome 1 (1999) no. 3, pp. 313-337. doi: 10.1007/s100970050009
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     title = {Effective {Nullstellensatz} for arbitrary ideals},
     journal = {Journal of the European Mathematical Society},
     pages = {313--337},
     year = {1999},
     volume = {1},
     number = {3},
     doi = {10.1007/s100970050009},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970050009/}
}
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