Speaker: 刘文飞教授，厦门大学

Inviter: 陈亦飞副研究员

Title: On numerically and cohomologically trivial automorphisms of properly elliptic surface

Language: Chinese

Time & Venue: 2024.11.22 14:00-15:00 思源楼 S723

Abstract: A proper elliptic surface is an elliptic surface f:S→B with Kodaira dimension κ(S)=1 (over the complex numbers for this talk). Recall that an automorphism of S is called numerically trivial (resp. cohomologically trivial) if it acts trivially on H*(S,Q) (resp. H*(S,Z)). It has been believed since long time that a properly elliptic surface S does not have any numerically trivial automorphisms if the geometric genus p_g(S)>0; and cohomologically trivial automorphisms do not exist even when p_g(S)=0. Surprisingly, we have found recently examples of properly elliptic surfaces with an arbitrarily large numerical trivial (resp. nontrivial cohomologically trivial) automorphism group, which invalidates the above claims. In this talk, I will present these examples, and then give certain bound and classification of them. Based on joint work with Fabrizio Catanese, Matthias Schütt, and partly with Christian Gleißner and Davide Frapporti.