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arXiv · 1109.4105

On Lagrangian fibrations by Jacobians II

Justin Sawon
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Abstract

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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Justin Sawon. 2011-09-19. On Lagrangian fibrations by Jacobians II. https://doi.org/10.1142/s0219199714500461

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