## Olivier Debarre ; Alexander Kuznetsov - Gushel--Mukai varieties: intermediate Jacobians

epiga:6475 - Épijournal de Géométrie Algébrique, December 17, 2020, Volume 4 - https://doi.org/10.46298/epiga.2020.volume4.6475
Gushel--Mukai varieties: intermediate Jacobians

Authors: Olivier Debarre ; Alexander Kuznetsov

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.

Volume: Volume 4
Published on: December 17, 2020
Accepted on: November 5, 2020
Submitted on: May 14, 2020
Keywords: Mathematics - Algebraic Geometry,14J45, 14J35, 14J40, 14M15