One remark on polynomials in two variables

Enrique Artal Bartolo and Pierrette Cassou-Noguès

Vol. 176 (1996), No. 2, 297–309

DOI: 10.2140/pjm.1996.176.297

Abstract

In this paper, we study some topological properties of rational polynomial maps f : ℂ² → ℂ. One can extend f to a map φ : X → ℙ¹ where X is a smooth algebraic compactification of ℂ². The behaviour of φ on the curve 𝒟 := X ∖ ℂ² contains all the information on the topology of f at infinity. We study the relationship between the so-called horizontal componentes of 𝒟, i.e., irreducible components D of 𝒟 such that ϕ_|D is surjective.

Mathematical Subject Classification 2000

Primary: 32J05

Secondary: 14E05

Milestones

Received: 20 May 1994

Published: 1 December 1996