On the parameter dependence of the real cubic surfaces in arnold's form

Manuel Falconi, Ernesto A. Lacomba, Jaume Llibre

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1 Citation (Scopus)

Abstract

We consider the topological classification of cubic surfaces which are obtained as intersection of the sphere S 3 with the algebraic variety defined by the zeroes of a homogeneous cubic polynomial in Arnold's normal form. This classification is based on the parameters appearing in this normal form, obtaining a correspondence between the parameters of the surface and its topological type. General classifications of cubic surfaces are made in the projective space ℙ 3(ℝ), but our method, based on a very simple combinatorial procedure is easier to implement in S 3. We split the cubic surfaces parameter space into ten equivalence classes. © 2004 Springer.
Original languageEnglish
Pages (from-to)153-164
JournalRendiconti del Circolo Matematico di Palermo
Volume53
DOIs
Publication statusPublished - 1 Jun 2004

Keywords

  • Cubic surface in S 3

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