On the birational gonalities of smooth curves
E. Ballico
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014), / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality sr(C) of C is the minimal integer t such that there is L∈Pict(C) with h0(C,L)=r+1. Fix an integer r≥3. In this paper we prove the existence of an integer gr such that for every integer g≥gr there is a smooth curve C of genus g with sr+1(C)/(r+1)>sr(C)/r, i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails.

Publié le : 2014-01-01
EUDML-ID : urn:eudml:doc:289735 
@article{bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_11,
     author = {E. Ballico},
     title = {On the birational gonalities of smooth curves},
     journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
     volume = {68},
     year = {2014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_11}
}

E. Ballico. On the birational gonalities of smooth curves. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 68 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2014_68_1_11/

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.