Research Article

The T-function of a parametric curve

Published in: Quaestiones Mathematicae
Volume 45 , issue 5 , 2022 , pages: 797–825

DOI: 10.2989/16073606.2021.1895899

Author(s): Sonia Pérez-Díaz , Spain

Keywords: 14Q05 , 14H50 , 14H20 , 14Q05 , 14H50 , 14H20

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.

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