论文标题
有限的多元多项式系统在有限场上的分布
The distribution of defective multivariate polynomial systems over a finite field
论文作者
论文摘要
本文介绍了代数品种的属性，该属性被定义为“缺陷”多元多项式序列的零序列。我们考虑两种类型的品种：理想理论完整的交集和绝对不可还原品种。对于这些类型，我们在任意字段上在每种类型的缺陷系统集合的维度上建立了改进的界限。另一方面，我们在有限场上的每种类型的系统数量上建立了改进的上限。
This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely irreducible varieties. For these types, we establish improved bounds on the dimension of the set of deficient systems of each type over an arbitrary field. On the other hand, we establish improved upper bounds on the number of systems of each type over a finite field.
