We relate the minimal gonality of smooth curves in a complete, ample, base point free linear system $|L|$
on an Enriques surface to the existence of certain secant spaces on the image of the surface mapped by the
adjoint system. We also explicitly compute the minimal gonality in terms of invariants of the line
bundle $L$. In particular, we obtain a precise criterion for the variation of the gonality of the curves.
Publié le : 2009-12-15
Classification:
Enriques surfaces,
line bundles,
curves,
gonality,
higher order embeddings,
14H51,
14C20,
14J28,
14J05,
14F17
@article{1260369406,
author = {Knutsen, Andreas Leopold},
title = {On secant spaces to Enriques surfaces},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {16},
number = {1},
year = {2009},
pages = { 907-931},
language = {en},
url = {http://dml.mathdoc.fr/item/1260369406}
}
Knutsen, Andreas Leopold. On secant spaces to Enriques surfaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp. 907-931. http://gdmltest.u-ga.fr/item/1260369406/