Modul:   MAT770  Oberseminar: Algebraische Geometrie

Torsion points of sections of Lagrangian fibrations and the Chow ring of hyper-Kähler manifolds

Vortrag von Prof. Dr. Claire Voisin

Datum: 04.12.17  Zeit: 13.15 - 14.45  Raum: Y27H25

Given a family of abelian varieties over a base B, with a section s, one may wonder if the set of points b where s(b) is a torsion point is non empty or even dense in B. This makes sense particularly when the dimension of the base is at least the dimension of the fiber, as the answer is then expected to be yes, under some transversality assumptions. I will explain a criterion due to André-Corvaja-Zannier guaranteeing that density holds. I will then discuss an application to Beauville's conjecture on the Chow ring of Hyper-Kähler manifolds (which presently works up to dimension 8).