The T-function of a parametric curve
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 polynomia...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49498 |
| Acceso en línea: | http://hdl.handle.net/10017/49498 https://dx.doi.org/10.2989/16073606.2021.1895899 |
| Access Level: | acceso abierto |
| Palabra clave: | Singularities of an algebraic curve Multiplicity of a point Resultant T-function Fibre function Rational curve parametrization Matemáticas Mathematics |
| Sumario: | 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. |
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