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

Laurent Busé (1) , Guillaume Chèze (2)

1 GALAAD - Geometry, algebra, algorithms
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]; Calcul formel [cs.SC]

Laurent Busé, Guillaume Chèze. On the total order of reducibility of a pencil of algebraic plane curves. 2008. ⟨hal-00348561v1⟩