On symplectic automorphisms of elliptic surfaces acting on CH0
On symplectic automorphisms of elliptic surfaces acting on CH0
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DOI：
10.1007/s11425-021-1950-3
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Jia-Li Du;Wenfei Liu
中科院分区：
文献类型：
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作者：
Jia-Li Du;Wenfei Liu
设S是复的科代拉一维光滑射影曲面。证明了辛自同构群Auts（S）平凡地作用在第0个Chow群CHo（S）的Albanese核CHo（S）上，除非几何亏格和不规则性满足ypg（S）=q（S）∈ {1，2}.在特殊情况下，同态Auts（S）→ Aut（CHo（S）alb）的象的阶数至多为3。我们的论证实际上考虑了椭圆曲面f：S → B的保纤维自同构群Autf（S）.我们证明了：如果σ∈ Autf（S）在Hi，0（S）（i> 0）上诱导平凡作用，则它在CH 0（S）α b上诱导平凡作用.作为副产品，我们得到：如果S是椭圆K3曲面，则Autf（S）∈ Auts（S）在CH 0（S）α b上平凡作用.
LetSbe 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 CHo(S)albof the 0-th Chow group CHo(S), unless possibly if the geometric genus and the irregularity satisfypg(S) =q(S) ∈ {1, 2}. In the exceptional cases, the image of the homomorphism Auts(S) → Aut(CHo(S)alb) has the order at most 3. Our arguments actually take care of the groupAutf(S) of fibration-preserving automorphisms of elliptic surfacesf:S → B.We prove that ifσ∈ Autf(S) induces the trivial action onHi,0(S) fori> 0, then it induces the trivial action on CH0(S)alb. As a by-product we obtain that ifSis an elliptic K3 surface, then Autf(S)∩Auts(S) acts trivially on CH0(S)alb.