Finite fiberwise bimeromorphic group actions on holomorphic conic bundles without degree-one divisors are always subgroups of Z/2Z times Z/2Z.
Automorphism groups of compact complex surfaces
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abstract
We study automorphism groups and birational automorphism groups of compact complex surfaces. We show that the automorphism group of such 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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Fiberwise bimeromorphic maps of conic bundles
Finite fiberwise bimeromorphic group actions on holomorphic conic bundles without degree-one divisors are always subgroups of Z/2Z times Z/2Z.