Lagrangian families of hyper-Kähler manifolds
Chenyu Bai
2022-07-05 14:00-15:00
ZOOM
Speaker: Chenyu Bai (Université de Paris)Time: 14:00-15:00 July 5, 2022 (Tuesday)
Place: Online (Zoom ID: 4663562952 Password: mcm1234)
Title: Lagrangian families of hyper-Kähler manifolds
Abstract: Hyper-Kähler manifolds form building blocks of compact Kähler manifolds with zero first Chern class, according to the Beauville–Bogomolov decomposition theorem. They are higher dimensional generalizations of K3 surfaces. Motivated by the conjectural plan proposed by Beauville and Voisin on the algebraic cycles in projective hyper-Kähler manifolds, we propose to consider the following question: given two Lagrangian subvarieties that can be deformed from one to the other in a projective hyper-Kähler manifold, are they necessarily rationally equivalent? I will try explain why we consider this question, to what extent we may expect it gives a positive answer, and why it gives in general a negative answer, adding to the subtlety of Voisin's conjecture.
