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

Source 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 $|G|<81(K_S^2)^3$.