HAL - INRIA :: [hal-00348561, version 2] On the total order of reducibility of a pencil of algebraic plane curves

hal-00348561, version 2

On the total order of reducibility of a pencil of algebraic plane curves

Journal of Algebra 341, 1 (2011) 256-278

Abstract: In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil is here counted with its appropriate multiplicity. It is proved that this number of reducible curves, counted with multiplicity, is bounded by d^2-1 where d is the degree of the pencil. Then, a sharper bound is given by taking into account the Newton's polygon of the pencil.

1: GALAAD (INRIA Sophia Antipolis)
INRIA – CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS)
2: Institut de Mathématiques de Toulouse (IMT)
Université Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées de Toulouse – CNRS : UMR5219

hal-00348561, version 2
http://hal.archives-ouvertes.fr/hal-00348561
oai:hal.archives-ouvertes.fr:hal-00348561
From: Laurent Busé <>
Submitted on: Wednesday, 17 August 2011 10:53:14
Updated on: Wednesday, 17 August 2011 13:54:23

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arXiv: 0812.4706

DOI: 10.1016/j.jalgebra.2011.06.006

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