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

Laurent Busé 1 Guillaume Chèze 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
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Submitted on : Wednesday, August 17, 2011 - 10:53:14 AM
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Laurent Busé, Guillaume Chèze. On the total order of reducibility of a pencil of algebraic plane curves. Journal of Algebra, Elsevier, 2011, 341 (1), pp.256-278. ⟨10.1016/j.jalgebra.2011.06.006⟩. ⟨hal-00348561v2⟩

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