English

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}
}

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11 pages