On Lagrangian fibrations by Jacobians I
Algebraic Geometry
2015-12-01 v3
Abstract
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.
Cite
@article{arxiv.0803.1186,
title = {On Lagrangian fibrations by Jacobians I},
author = {Justin Sawon},
journal= {arXiv preprint arXiv:0803.1186},
year = {2015}
}
Comments
28 pages, 1 figure, the article has been extensively rewritten (Section 2 is completely new and numerous other lemmas and remarks have been added to Sections 3 and 4), the `mild singularities' hypothesis on the curves has been replaced by the simpler hypothesis that the curves are Gorenstein, the lower bound of 4n+2 for the degree of the discriminant locus is also new