Mordell-Weil Groups of Linear Systems and the Hitchin Fibration
Algebraic Geometry
2017-06-30 v1 Differential Geometry
Abstract
In this paper, we study rational sections of the relative Picard scheme of a linear system on a smooth projective variety. We prove that if the linear system is basepoint-free and the locus of non-integral divisors has codimension at least two, then all rational sections of the relative Picard scheme come from restrictions of line bundles on the variety. As a consequence, we describe the group of sections of the Hitchin fibration for moduli spaces of Higgs bundles on curves.
Keywords
Cite
@article{arxiv.1706.09515,
title = {Mordell-Weil Groups of Linear Systems and the Hitchin Fibration},
author = {Matthew Woolf},
journal= {arXiv preprint arXiv:1706.09515},
year = {2017}
}
Comments
11 pages