RT info:eu-repo/semantics/article
T1 The T-function of a parametric curve
A1 Pérez Díaz, Sonia
K1 Singularities of an algebraic curve
K1 Multiplicity of a point
K1 Resultant
K1 T-function
K1 Fibre function
K1 Rational curve parametrization
K1 Matemáticas
K1 Mathematics
AB In this paper, we introduce the T–function, T(s), which is a polynomial defined by means of a univariate resultant constructed froma given parametrization P(t) ∈ K(t)n, n ≥ 2 of an algebraic spacecurve C. It is shown that T(s) = Qni=1 HPi(s)mi−1, where HPi(s), i =1, . . . , n are polynomials (the fibre functions) whose roots are the fibreof the ordinary singularities Pi ∈ C of multiplicity mi, i = 1, . . . , n ofC. Therefore, a complete classification of the singularities of C, via thefactorization of a resultant, is obtained.
PB Taylor & Francis
SN 1607-3606
YR 2021
FD 2021-03-01
LK http://hdl.handle.net/10017/49498
UL http://hdl.handle.net/10017/49498
LA eng
NO Agencia Estatal de Investigación
DS MINDS@UW
RD 24-abr-2024