## 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

### Keywords:

Renegar’s $$U$$-resultant; affine Bézout inequality
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### References:

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