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Displaying similar documents to “Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane.”

Enumerative geometry of divisorial families of rational curves

Ziv Ran (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We compute the number of irreducible rational curves of given degree with 1 tacnode in 2 or 1 node in 3 meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree d passing through 3 d - 2 given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.

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.

Trivial points on towers of curves

Xavier Xarles (2013)

Journal de Théorie des Nombres de Bordeaux

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In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.