Abstract
It is proved that for a complex minimal smooth projective surface S of general type, its abelian automorphism group is of order , provided χ(Os) ≥ 315 (resp. the canonical map of S is composed with a pencil of curves and χ(Os) ≥ 21, where Ks is the canonical divisor of S, and χ(Os) is the Euler characteristic of the structure sheaf of S.
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