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On Lagrangian fibrations by Jacobians, II

Justin Sawon

Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA

www.unc.edu/~sawon.

https://doi.org/10.1142/S0219199714500461Cited by:3 (Source: Crossref)

Abstract

Let Y → ℙⁿ be a flat family of reduced Gorenstein curves, such that the compactified relative Jacobian 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.

Keywords:

AMSC: 14J28, 14D06, 53C26

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