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arXiv · 1906.00231

Elimination ideals and Bezout relations

Andre Galigo·Zbigniew Jelonek
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Abstract

Let $k$ be an infinite field and $I\subset k [x_1, \ldots ,x_n]$ be an ideal such that dim $V(I)=q$. Denote by $(f_1, \ldots, f_s)$ a set of generators of $I$. One can see that in the set $I\cap k [x_{1},...,x_{q+1}]$ there exist non-zero polynomials, depending only on these $q+1$ variables. We aim to bound the minimal degree of the polynomials of this type, and of a B\'ezout (i.e. membership) relation expressing such a polynomial as a combination of the $f_i$.

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Andre Galigo, Zbigniew Jelonek. 2019-06-01. Elimination ideals and Bezout relations. https://arxiv.org/abs/1906.00231

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