Pinceaux de courbes planes et invariants polaires

Evelia R. García Barroso¹ ; Arkadiusz Płoski²

¹ Departamento de Matemática Fundamental Facultad de Matemáticas Universidad de La Laguna 38271 La Laguna, Tenerife, España
² Department of Mathematics Technical University Al. 1000 L PP 7 25-314 Kielce, Poland

Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 113-128.

Résumé

We study pencils of plane curves $f_t=f-tl^N$, $t\in {\mathbb C}$, using the notion of polar invariant of the plane curve $f=0$ with respect to a smooth curve $l=0$. More precisely we compute the jacobian Newton polygon of the generic fiber $f_t$, $t\in {\mathbb C}$. The main result gives the description of pencils which have an irreducible fiber. Furthermore we prove some applications of the local properties of pencils to singularities at infinity of polynomials in two complex variables.

Détail

DOI : 10.4064/ap83-2-3

Mots-clés : study pencils plane curves f tl mathbb using notion polar invariant plane curve respect smooth curve precisely compute jacobian newton polygon generic fiber mathbb main result gives description pencils which have irreducible fiber furthermore prove applications local properties pencils singularities infinity polynomials complex variables