Theta Groups and Products of Abelian and Rational Varieties

By Yuri G. Zarhin. Proceedings of the Edinburgh Mathematical Society, 2010

58 citations recorded by the source corpus.

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 posed by Vladimir L. Popov.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/390671ed6260cc1db148246466488b19263d1304

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

Singularities of linear systems and boundedness of Fano varieties (2016, background): “Another consequence of Theorem 1.1 is the following uniform Jordan property of birational automorphism groups of rationally connected varieties.”
Jordan property for Cremona groups (2012, background): “Zarhin [32]) Suppose that X ∼= E×P1, where E is an abelian variety of dimension dim(E)> 0.”
Jordan groups and automorphism groups of algebraic varieties (2013, background): “X/ for algebraic varieties X has generated interest of algebraic geometers in Moscow among whom I have promoted it, and led to a further progress in Problem B (hence A as well) in papers [49, 50, 62].”