  Let Y->P^n be a flat family of integral Gorenstein curves, such that the
compactified relative Jacobian X=\bar{J}^d(Y/P^n) is a Lagrangian fibration. We
prove that the degree of the discriminant locus Delta in P^n is at least 4n+2,
and we prove that X is a Beauville-Mukai integrable system if the degree of
Delta is greater than 4n+20.
