The limit point and the T-function
Let P(t) ϵ P2 (K(t)) be a rational projective parametrization of a plane curve C. In this paper, we introduce the notion of limit point, PL, of P(t), and some remarkable properties of PL are obtained. In particular, if the singularities of C are P1, . . . , Pn and PL (all of them ordinary) and their...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/41538 |
| Acceso en línea: | http://hdl.handle.net/10017/41538 https://dx.doi.org/10.1016/j.jsc.2018.06.009 |
| Access Level: | acceso abierto |
| Palabra clave: | Algebraic parametric curve Rational parametrization Singularities Limit point T-function Fibre Function Matemáticas Mathematics |
| Sumario: | Let P(t) ϵ P2 (K(t)) be a rational projective parametrization of a plane curve C. In this paper, we introduce the notion of limit point, PL, of P(t), and some remarkable properties of PL are obtained. In particular, if the singularities of C are P1, . . . , Pn and PL (all of them ordinary) and their respective multiplicities are m1, . . . , mn and mL, we show that T(s) = n i=1 HPi (s) m-1HPL (s) mL-1 , where T(s) is the univariate resultant of two polynomials obtained from P(t), and HP1 (s), . . . , HPn (s), HPL (s) are the fibre functions of the singularities. The fibre function of a point P is a polynomial HP (s) whose roots are the fibre of P. Thus, a complete classification of the singularities of a given plane curve, via the factorization of a resultant, is obtained. |
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