Abstract

In this paper, we introduce the T-function, T(s), which is a polynomial defined by means of a univariate resultant constructed from a given parametrization of an algebraic space curve . It is shown that , where are polynomials (the fibre functions) whose roots are the fibre of the ordinary singularities of multiplicity . Therefore, a complete classification of the singularities of , via the factorization of a resultant, is obtained.

中文翻译：

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参数曲线的 T 函数

摘要

在本文中，我们介绍了T 函数T ( s ) ，它是一个多项式，由代数空间曲线的给定参数化构造的单变量结果定义。证明, 其中是 多项式 (纤 函数) , 其 根 是 普通的 多重奇点 的 纤. 因此，通过对结果进行因式分解，得到的奇点的完整分类。