Displaying similar documents to “On triple curves through a rational triple point of a surface”

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.

Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin (2014)

Open Mathematics

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Let 𝕜 be a field of characteristic zero and G be a finite group of automorphisms of projective plane over 𝕜 . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field 𝕜 is algebraically closed. In this paper we prove that ℙ 𝕜 2 ℙ 𝕜 2 G G is rational for an arbitrary field 𝕜 of characteristic zero.

On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov, Viktor Kulikov (2013)

Open Mathematics

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The article contains a new proof that the Hilbert scheme of irreducible surfaces of degree m in ℙm+1 is irreducible except m = 4. In the case m = 4 the Hilbert scheme consists of two irreducible components explicitly described in the article. The main idea of our approach is to use the proof of Chisini conjecture [Kulikov Vik.S., On Chisini’s conjecture II, Izv. Math., 2008, 72(5), 901–913 (in Russian)] for coverings of projective plane branched in a special class of rational curves. ...