Finite fiberwise bimeromorphic group actions on holomorphic conic bundles without degree-one divisors are always subgroups of Z/2Z times Z/2Z.
Complex tori, theta groups and their Jordan properties
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abstract
We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups does not hold for the group of bimeromorphic automorphisms of a product of the complex projective line and a complex torus of positive algebraic dimension.
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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.