Strong Franchetta Conjecture for Linear Systems
  In this paper, we study rational sections of the relative Picard variety of a linear system on a smooth projective variety. Specifically, 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 variety come from restrictions of line bundles on the variety. 
Matthew Woolf
math.AG