PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

2014 | 68 | 1 |
Tytuł artykułu

### On the birational gonalities of smooth curves

Autorzy
Treść / Zawartość
Warianty tytułu
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
Rocznik
Tom
Numer
Opis fizyczny
Daty
wydano
2014
online
2015-05-23
Twórcy
autor
Bibliografia
• Coppens, M., Martens, G., Linear series on 4-gonal curves, Math. Nachr. 213, no. 1 (2000), 35–55.
• Eisenbud, D., Harris, J., On varieties of minimal degree (a centennial account), Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 3–13, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.
• 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.
Typ dokumentu
Bibliografia
Identyfikatory