Hyper-Kaehler compactification of the intermediate Jacobian fibration of a cubic fourfold : the twisted case

Claire Voisin

Published 2016-11-21Version 1

This inaugural note provides first of all a short survey of hyper-Kaehler geometry, then an introduction to my recent paper with Laza and Sacc\`a on the construction of deformations of O'Grady's $10$-dimensional manifolds as compactifications of intermediate Jacobian fibrations associated to cubic fourfolds, and finally a complement to that paper consisting in the analogous construction in the twisted case, leading to isogenous but presumably not isomorphic or birational hyper-Kaehler manifolds.