%0 Journal Article 
%A Pérez Díaz, Sonia
%T The T-function of a parametric curve
%D 2021
%@ 1607-3606
%U http://hdl.handle.net/10017/49498
%X 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 P(t) ∈ K(t)
n
, n ≥ 2 of an algebraic space
curve C. It is shown that T(s) = Qn
i=1 HPi
(s)
mi−1
, where HPi
(s), i =
1, . . . , n are polynomials (the fibre functions) whose roots are the fibre
of the ordinary singularities Pi ∈ C of multiplicity mi
, i = 1, . . . , n of
C. Therefore, a complete classification of the singularities of C, via the
factorization of a resultant, is obtained.
%K Singularities of an algebraic curve
%K Multiplicity of a point
%K Resultant
%K T-function
%K Fibre function
%K Rational curve parametrization
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala