On triple curves through a rational triple point of a surface

M. R. Gonzalez-Dorrego

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

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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.

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

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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 $ℙ_{𝕜}^{2} / G$ is rational for an arbitrary field $𝕜$ of characteristic zero.

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On the irreducibility of Hilbert scheme of surfaces of minimal degree

Fedor Bogomolov, Viktor Kulikov (2013)

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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. ...