Seminar: On numerically trivial automorphisms of compact hyperkähler 4-manifolds

Seminar| Institute of Mathematical Sciences

Abstract: An automorphism of a complex projective variety X is called numerically trivial if it acts trivially on the cohomology ring H^* (X,Q), and they form a subgroup of automorphisms, which we denote by Aut_Q (X). It is well known that Aut_Q (X) is trivial when X is a K3 surface. A natural question is whether or not the same holds true for compact hyperkähler manifolds, which are generalization of K3 surfaces. This has since been positively answered for the known examples of compact hyperkähler manifolds in the works of Beauville, Oguiso, and Mongardi-Wandel. Since the (topological) classification of hyperkähler manifolds is still lacking, a more conceptual proof without referring to the explicit construction of the manifolds is needed to address the general situation. In this talk, after recalling some background, I will show that  Aut_Q (X) is trivial for any compact hyperkähler 4-manifold. This is joint work with JIANG Chen.