Theta groups and products of abelian and rational varieties
Yuri G. Zarhin

TL;DR
This paper demonstrates that Jordan's theorem does not extend to the birational automorphism groups of certain algebraic varieties, specifically products of elliptic curves and the projective line, answering a question in algebraic geometry.
Contribution
It shows the failure of Jordan's theorem analogue for birational automorphism groups of specific product varieties, providing a negative result in algebraic geometry.
Findings
Jordan's theorem does not hold for these groups
Negative answer to Popov's question
Counterexamples in birational automorphism groups
Abstract
We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups does not hold for the groups of birational automorphisms of products of an elliptic curve and the projective line. This gives a negative answer to a question of V. L. Popov, arXiv:1001.1311 [math.AG].
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