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TitleOn the parameter dependence of the real cubic surfaces in Arnold
Author(s) Manuel Falconi, Ernesto A. Lacomba, Jaume Llimbre
TypeArticle in Journal
AbstractWe consider the topological classification of cubic surfaces which are obtained as intersection of the sphere𝕊3 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 ℙ3(ℝ), but our method, based on a very simple combinatorial procedure is easier to implement in𝕊3. We split the cubic surfaces parameter space into ten equivalence classes.
KeywordsCubic surface in𝕊3
ISSN0009-725X; 1973-4409/e
URL http://link.springer.com/article/10.1007%2FBF02872868
LanguageEnglish
JournalRend. Circ. Mat. Palermo (2)
Volume53
Number2
Pages153--164
PublisherSpringer, Milan; Circolo Matematico di Palermo, Palermo
Year2004
Edition0
Translation No
Refereed No
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