Displaying similar documents to “A really elementary proof of real Lüroth's theorem.”

Rational Bézier curves with infinitely many integral points

Petroula Dospra (2023)

Archivum Mathematicum

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In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.

Periodic solitons and real algebraic curves.

S. M. Natanzon (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We describe a method of calculation of all physical algebraic-geometrical solutions of KP-equations.

Optimal degree construction of real algebraic plane nodal curves with prescribed topology. I. The orientable case.

Francisco Santos (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We study a constructive method to find an algebraic curve in the real projective plane with a (possibly singular) topological type given in advance. Our method works if the topological model T to be realized has only double singularities and gives an algebraic curve of degree 2N+2K, where N and K are the numbers of double points and connected components of T. This degree is optimal in the sense that for any choice of the numbers N and K there exist models which cannot be realized algebraically...