Symplectic automorphisms of a surface with genus two fibration and their action on CH0
Abstract
Let S be a complex smooth projective surface with a genus two fibration, and Aut s (S) the group of symplectic automorphisms, fixing every holomorphic 2-forms (if any) on S. Based on the work of Jin-Xing Cai, we show that, if χ(O S ) ≥ 5, then |Aut s (S)| ≤ 2. Then we verify, under some conditions, that Aut s (S) acts trivially on the Albanese kernel CH 0 (S) alb of the 0-th Chow group, which is predicted by a conjecture of Bloch and Beilinson.As a consequence, if an automorphism σ ∈ Aut(S) acts trivially on H i,0 (S) for 0 ≤ i ≤ 2, then it also acts trivially on CH 0 (S) alb .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Pacific Journal of Mathematics
- Volume
- 342
- Issue
- 2
- Pages
- 259–273
- Publication date
- 23 April 2026
- Language
- EN