On Lagrangian fibrations by Jacobians I

What is it about?

Let Y → P^n be a flat family of integral Gorenstein curves, such that the compactified relative Jacobian X = J̅^d(Y/P^n) is a Lagrangian fibration. We prove that the degree of the discriminant locus Δ ⊂ P^n is at least 4n + 2, and we prove that X is a Beauville–Mukai integrable system if deg Δ > 4n + 20.

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