Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Pinceaux de courbes planes et invariants polaires

Tom 83 / 2004

Annales Polonici Mathematici 83 (2004), 113-128 MSC: Primary 32S55; Secondary 14H20. DOI: 10.4064/ap83-2-3

Streszczenie

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.

Autorzy

• Evelia R. García BarrosoDepartamento de Matemática Fundamental
38271 La Laguna, Tenerife, España
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