On Lagrangian fibrations by Jacobians I

Details On Lagrangian fibrations by Jacobians I On Lagrangian fibrations by Jacobians I

2008-03-07

arxiv.org/abs/0803.1186v3

Mathematics

Algebraic Geometry

28 pages, 1 figure, the article has been extensively rewritten (Section 2 is completely new and numerous other lemmas and rema

Scientific paper

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.

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