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arXiv · 2609.21505

Bounds on automorphism groups of surfaces of general type with negative c_2

Xiaokun Zhong
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Abstract

Let $k$ be an algebraically closed field of characteristic $p>0$, and let $S$ be a minimal smooth projective surface of general type over $k$. If the second Chern class satisfies $c_2(S)<0$, then the order of the automorphism group satisfies $|\mathrm{Aut}_k(S)|<2598(K_S^2)^4$, and the order of every abelian subgroup $G\subset \mathrm{Aut}_k(S)$ satisfies $|G|<81(K_S^2)^3$.

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Xiaokun Zhong. 2026-09-18. Bounds on automorphism groups of surfaces of general type with negative c_2. https://arxiv.org/abs/2609.21505

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