On Lagrangian fibrations by Jacobians I
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Justin Sawon
Abstract
Let Y → ℙn be a flat family of integral Gorenstein curves, such that the compactified relative Jacobian X = J̅d(Y/ℙn) is a Lagrangian fibration. We prove that the degree of the discriminant locus Δ ⊂ ℙn is at least 4n + 2, and we prove that X is a Beauville–Mukai integrable system if deg Δ > 4n + 20.
The author would like to thank Fabrizio Catanese, Brendan Hassett, Jun-Muk Hwang, Stefan Kebekus, Manfred Lehn, Dimitri Markushevich, Rick Miranda, Keiji Oguiso, and Christian Thier for many helpful discussions on the material presented here, and is grateful for the hospitality of the Max-Planck-Institut für Mathematik, Bonn, and the Institute for Mathematical Sciences, the Chinese University of Hong Kong, where these results were obtained.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
- A Satake isomorphism for representations modulo p of reductive groups over local fields
- Quantum Grothendieck rings and derived Hall algebras
- On Lagrangian fibrations by Jacobians I
- From exceptional collections to motivic decompositions via noncommutative motives
- Branched Willmore spheres
- Mori dream spaces of Calabi–Yau type and log canonicity of Cox rings
- On inductively free reflection arrangements
- Willmore surfaces in 3-sphere foliated by circles
Artikel in diesem Heft
- Frontmatter
- Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
- A Satake isomorphism for representations modulo p of reductive groups over local fields
- Quantum Grothendieck rings and derived Hall algebras
- On Lagrangian fibrations by Jacobians I
- From exceptional collections to motivic decompositions via noncommutative motives
- Branched Willmore spheres
- Mori dream spaces of Calabi–Yau type and log canonicity of Cox rings
- On inductively free reflection arrangements
- Willmore surfaces in 3-sphere foliated by circles
