On symplectic automorphisms of elliptic surfaces acting on CH_(0)  

作　　者：Jiabin Du Wenfei Liu 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Science China Mathematics》2023年第3期443-456,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11971399 and 11771294);the Presidential Research Fund of Xiamen University(Grant No.20720210006)。

摘　　要：Let S be a complex smooth projective surface of Kodaira dimension one. We show that the group Auts(S) of symplectic automorphisms acts trivially on the Albanese kernel CH_(0)(S)albof the 0-th Chow group CH_(0)(S), unless possibly if the geometric genus and the irregularity satisfy pg(S) = q(S) ∈ {1, 2}. In the exceptional cases, the image of the homomorphism Auts(S) → Aut(CH_(0)(S)alb) has the order at most 3. Our arguments actually take care of the group Autf(S) of fibration-preserving automorphisms of elliptic surfaces f : S → B. We prove that if σ ∈ Autf(S) induces the trivial action on Hi,0(S) for i > 0, then it induces the trivial action on CH_(0)(S)alb. As a by-product we obtain that if S is an elliptic K3 surface, then Autf(S)∩Auts(S)acts trivially on CH_(0)(S)alb.

关 键 词：symplectic automorphism elliptic surface Chow group 

分 类 号：O157.5[理学—数学]