On Lagrangian fibrations by Jacobians II
Algebraic Geometry
2015-12-01 v1
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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Cite
@article{arxiv.1109.4105,
title = {On Lagrangian fibrations by Jacobians II},
author = {Justin Sawon},
journal= {arXiv preprint arXiv:1109.4105},
year = {2015}
}
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33 pages