On Lagrangian fibrations by Jacobians II

Details On Lagrangian fibrations by Jacobians II On Lagrangian fibrations by Jacobians II

2011-09-19

arxiv.org/abs/1109.4105v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

Let Y->P^n be a flat family of reduced Gorenstein curves, such that the compactified relative Jacobian X=\bar{J}^d(Y/P^n) is a Lagrangian fibration. We prove that X is a Beauville-Mukai integrable system if n=3, 4, or 5, and the curves are irreducible and non-hyperelliptic. We also prove that X is a Beauville-Mukai system if n=3, d is odd, and the curves are canonically positive 2-connected hyperelliptic curves.

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