中国科学院数学与系统科学研究院
数学研究所
学术报告
代数几何研讨班
报告人: 刘文飞 教授（厦门大学）
题 目：On numerically and cohomologically trivial automorphisms of properly elliptic surfaces
时 间：2024.11.22（星期五）14：00-15：00
地 点：思源楼S723
摘 要：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.