Pinceaux de courbes planes et invariants polaires

Volume 83 / 2004

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


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.


  • Evelia R. García BarrosoDepartamento de Matemática Fundamental
    Facultad de Matemáticas
    Universidad de La Laguna
    38271 La Laguna, Tenerife, España
  • Arkadiusz PłoskiDepartment of Mathematics
    Technical University
    Al. 1000 L PP 7
    25-314 Kielce, Poland

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