Title: Mordell-Weil Groups of Linear Systems and the Hitchin Fibration,
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.