English

Gushel--Mukai varieties: intermediate Jacobians

Algebraic Geometry 2024-04-17 v4

Abstract

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

Cite

@article{arxiv.2002.05620,
  title  = {Gushel--Mukai varieties: intermediate Jacobians},
  author = {Olivier Debarre and Alexander Kuznetsov},
  journal= {arXiv preprint arXiv:2002.05620},
  year   = {2024}
}

Comments

48 pages. Latest addition to our series of articles on the geometry of Gushel-Mukai varieties; v2: minor stylistic improvements, results unchanged; v3: minor improvements; v4: final version, published in EPIGA

R2 v1 2026-06-23T13:41:02.313Z