Integrable systems from intermediate Jacobians of 5-folds

preprint2011arXivOpen access

Given a cubic 4-fold $Y$ , we provide an easy Hodge-theoretic proof of the following result of Iliev--Manivel: the relative intermediate Jacobian of the universal family of cubic 5-folds $Z$ extending $Y$ is a Lagrangian fibration.

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Integrable systems from intermediate Jacobians of 5-folds

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