Bloch's conjecture for symplectic autoequivalences on K3 surfaces
Prof. Zhiyuan Li
2023-04-03 14:00-15:00
MCM410
Speaker: Prof. Zhiyuan Li (Shanghai Center for Mathematical Sciences)Time: 14:00-15:00 April 3, 2023 (Monday)
Place: MCM410
Title: Bloch's conjecture for symplectic autoequivalences on K3 surfaces
Abstract: Bloch's conjecture for a surface X over an algebraically closed field k states that every homologically trivial correspondence acts as 0 on the Albanese kernel. When X is a K3 surface, this conjecture has been proved by Voisin and Huybrechts for symplectic automorphisms of finite order. In this talk, I will talk about the recent progress on Bloch's conjecture for symplectic autoequivalences on a K3 surface. In particular, we show that the conjecture holds for symplectic automorphisms of arbitrary order provided the Neron-Severi lattice is not a two twist. This also gives a new proof of Voisin's result on symplectic involutions. I will also mention the application to Bloch's conjecture for hyper-Kähler varieties. This is a joint work with X.Yu and R. Zhang.
