Abstract
Let S be a complex nonsingular minimal projective surface of general type. In this note we show that any automorphism of S of order three acts faithfully on \(H^2(S, \mathbb {Q})\) provided that \(q(S)\ge 3\). In the case \(q(S)=2\), the classification for surfaces with an automorphism of order 3 acting trivially on \(H^2(S, \mathbb Q)\) is given. We also construct surfaces S with such an automorphism.
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This work was supported by the NSFC (Nos. 11471020, 11971399).
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Cai, JX. Automorphisms of an irregular surface of general type acting trivially in cohomology, III. manuscripta math. 164, 489–507 (2021). https://doi.org/10.1007/s00229-020-01192-4
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DOI: https://doi.org/10.1007/s00229-020-01192-4