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Theta Groups and Products of Abelian and Rational Varieties

Published online by Cambridge University Press:  17 December 2013

Yuri G. Zarhin
Yuri G. Zarhin*
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA Department of Mathematics, Weizmann Institute of Science, POB 26, Rehovot 7610001, Israel (zarhin@math.psu.edu)
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Abstract

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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.

Keywords

birational automorphismsline bundlesabelian varietiesPrimary 14E07Secondary 14K05
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 299 - 304
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Mumford, D., On the equations defining abelian varieties, I, Invent. Math. 1 (1966), 287–354.Google Scholar
2.Mumford, D., Abelian Varieties, 2nd edn (Oxford University Press, 1974).Google Scholar
3.Popov, V. L., On the Makar–Limanov, Derksen invariants, and finite automorphism groups of algebraic varieties, in Affine Algebraic Geometry (The Russell Festschrift), CRM Proceedings and Lecture Notes, Volume 54, pp. 289–311 (American Mathematical Society, Providence, RI, 2011).Google Scholar
4.Shafarevich, I. R., Basic Algebraic Geometry, Volume II, 2nd edn (Springer, 1994).Google Scholar