C. Voisin - Cubic fourfolds, hyper-Kähler manifolds and their degenerations

Claire Voisin (1) , Jérémy Magnien (2)

1 Collège de France - Chaire Géométrie algébrique
2 IF - Institut Fourier

There at least three families of hyper-K ̈ahler manifolds built from cubic fourfolds, the most recently discovered one being the compactified intermediate Jacobian fibrations I constructed with Laza and Sacca. In a joint work with Koll ́ar, Laza and Sacca, we provide an easy way to compute their deformation types, by proving that if the central fiber of a degeneration of hyper-Kähler manifolds has one component which is not uniruled, then after base-change the family becomes fiberwise birational to a family of smooth hyper-Kähler manifolds.

Mots clés: Grenoble; Complex analytic and differential geometry 2017; cubic fourfolds; degenerations; hyper-Kähler manifolds

Domaines: Géométrie différentielle [math.DG]

Claire Voisin, Jérémy Magnien. C. Voisin - Cubic fourfolds, hyper-Kähler manifolds and their degenerations: Complex analytic and differential geometry 2017 . 2017. ⟨medihal-01615523⟩