When using resultants for elimination, one standard issue is that the resultant vanishes if the variety contains components of dimension larger than the expected dimension. J. Canny proposed an elegant construction, generalized characteristic polynomial, to address this issue by symbolically perturbing the system before the resultant computation. Such perturbed resultant would typically involve artefact components only loosely related to the geometry of the variety of interest. For removing these components, J.M. Rojas proposed to take the greatest common divisor of the results of two different perturbations. In this paper, we investigate this construction, and show that the extra components persistent under taking different perturbations must come either from singularities or from positive-dimensional fibers.

翻译：在使用结式进行消元时，一个标准问题是：若簇中包含维度高于预期维度的分量，则结式会消失。J. Canny 提出了一种精巧的构造——广义特征多项式，通过在结式计算前对系统进行符号扰动来应对这一问题。这类扰动结式通常会包含仅与被研究簇的几何结构松散相关的人造分量。为去除这些分量，J.M. Rojas 提出取两次不同扰动结果的极大公因子。本文研究这一构造，并证明在不同扰动下仍持久存在的额外分量必然源自奇异性或正维纤维。