1Departamento de Matemática Fundamental Facultad de Matemáticas Universidad de La Laguna 38271 La Laguna, Tenerife, España 2Department of Mathematics Technical University Al. 1000 L PP 7 25-314 Kielce, Poland
Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 113-128
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.
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
Affiliations des auteurs :
Evelia R. García Barroso
1
;
Arkadiusz Płoski
2
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
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title = {Pinceaux de courbes planes et invariants polaires},
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Evelia R. García Barroso; Arkadiusz Płoski. Pinceaux de courbes planes et invariants polaires. Annales Polonici Mathematici, Tome 83 (2004) no. 2, pp. 113-128. doi: 10.4064/ap83-2-3
