Density of orbits of dominant regular self-maps of semiabelian varieties

We prove a conjecture of Medvedev and Scanlon [Ann. of Math. (2), 179 (2014), no. 1, 81-177] in the case of regular morphisms of semiabelian varieties. That is, if G is a semiabelian variety defined over an algebraically closed field K of characteristic 0, and \varphi \colon G\to G is a dominant reg...

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Published in:Transactions of the American Mathematical Society 2019-05, Vol.371 (9), p.6341-6358
Main Authors: Ghioca, Dragos, Satriano, Matthew
Format: Article
Language:English
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Summary:We prove a conjecture of Medvedev and Scanlon [Ann. of Math. (2), 179 (2014), no. 1, 81-177] in the case of regular morphisms of semiabelian varieties. That is, if G is a semiabelian variety defined over an algebraically closed field K of characteristic 0, and \varphi \colon G\to G is a dominant regular self-map of G which is not necessarily a group homomorphism, we prove that one of the following holds: either there exists a nonconstant rational fibration preserved by \varphi or there exists a point x\in G(K) whose \varphi -orbit is Zariski dense in G.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7475