Brill-Noether theory of curves on Enriques surfaces I: the positive cone and gonality

Details Brill-Noether theory of curves on Enriques surfaces I: the positive cone and gonality Brill-Noether theory of curves on Enriques surfaces I: the positive cone and gonality

2008-03-28

arxiv.org/abs/0803.4098v1

Mathematics

Algebraic Geometry

To appear on Math.Z

Scientific paper

We study the existence of linear series on curves lying on an Enriques
surface and general in their complete linear system. Using a method that works
also below the Bogomolov-Reider range, we compute, in all cases, the gonality
of such curves. We also give a new result about the positive cone of line
bundles on an Enriques surface and we show how this relates to the gonality.

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