Birationally trivial real smooth cubic surfaces

Details Birationally trivial real smooth cubic surfaces Birationally trivial real smooth cubic surfaces

2010-10-02

arxiv.org/abs/1010.0294v1

Mathematics

Algebraic Geometry

6 pages

Scientific paper

Smooth real cubic surfaces are birationally trivial (over $\R$) if and only if their real locus is connected or, equivalently, if and only if they have two skew real lines or two skew complex conjugate lines. In such a case a parametrization over the reals can be given by cubic polynomials. In this short note we provide a simple geometric method to obtain such parametrization based in an algorithm by I. Polo-Blanco and J. Top \cite{Po-Top}.

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