On the birational gonalities of smooth curves

• Autorzy: E. Ballico
• Języki publikacji: EN

Abstrakty

EN

Let \(C\) be a smooth curve of genus \(g\). For each positive integer \(r\) the birational \(r\)-gonality \(s_r(C)\) of \(C\) is the minimal integer \(t\) such that there is \(L\in \mbox{Pic}^t(C)\) with \(h^0(C,L) =r+1\). Fix an integer \(r\ge 3\). In this paper we prove the existence of an integer \(g_r\) such that for every integer \(g\ge g_r\) there is a smooth curve \(C\) of genus \(g\) with \(s_{r+1}(C)/(r+1) > s_r(C)/r\), i.e. in the sequence of all birational gonalities of \(C\) at least one of the slope inequalities fails.

Słowa kluczowe

EN

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2014
• Tom: 68
• Numer: 1

Daty

wydano

2014

online

2015-05-23

Twórcy

autor

E. Ballico

Bibliografia

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• Harris, J., Eisenbud, D., Curves in projective space, Séminaire de Mathématiques Supérieures, 85, Presses de l’Université de Montréal, Montréal, Que., 1982.
• Hatshorne, R., Algebraic Geometry, Springer-Verlag, Berlin, 1977.
• Laface, A., On linear systems of curves on rational scrolls, Geom. Dedicata 90, no. 1 (2002), 127–144; generalized version in arXiv:math/0205271v2.
• Lange, H., Martens, G., On the gonality sequence of an algebraic curve, Manuscripta Math. 137 (2012), 457–473.

Identyfikatory

DOI

10.17951/a.2014.68.1.11