Pinceaux de courbes planes et invariants polaires
Volume 83 / 2004
Annales Polonici Mathematici 83 (2004), 113-128
MSC: Primary 32S55; Secondary 14H20.
DOI: 10.4064/ap83-2-3
Abstract
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.
