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Working paper

Gushel--Mukai varieties: intermediate Jacobians

Kuznetsov A. G., Debarre O.
We describe intermediate Jacobians of Gushel-Mukai varieties X of dimensions 3 or 5: if A is the Lagrangian space associated with X, we prove that the intermediate Jacobian of X is isomorphic to the Albanese variety of the canonical double covering of any of the two dual Eisenbud-Popescu-Walter surfaces associated with A. As an application, we describe the period maps for Gushel-Mukai threefolds and fivefolds.