Automorphism Groups of Compact Complex Surfaces

Abstract We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such a surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational to a product of an elliptic and a rational curve.

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Bibliographic Details
Published in:International mathematics research notices 2021-07, Vol.2021 (14), p.10490-10520
Main Authors: Prokhorov, Yuri, Shramov, Constantin
Format: Article
Language:English
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Summary:Abstract We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such a surface $X$ is always Jordan, and the birational automorphism group is Jordan unless $X$ is birational to a product of an elliptic and a rational curve.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnz124