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On the affine Bezout inequality. (English) Zbl 0861.14001

The aim of the paper is to give an elementary proof of the so-called affine Bézout inequality: “The set in \(\overline k^n\) of all common zeroes of the polynomials \(f_1, \dots, f_n \in k[X_1, \dots, X_n]\) is either infinite or has at most \((\deg f_1) \dots (\deg f_n)\) elements \((\overline k\) indicating the algebraic closure of the field \(k)\)”.

MSC:

14A05 Relevant commutative algebra
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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References:

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