Gushel-Mukai varieties: intermediate Jacobians
Résumé
Let X be a Gushel-Mukai variety of dimension 3 or 5. If A ⊂ 3 V 6 is the Lagrangian subspace 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 Y ≥2 A and Y ≥2 A ⊥. As an application, we describe the period maps for Gushel-Mukai varieties of dimension 3 or 5.
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