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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Dragos Ghioca and Matthew Satriano
Journal: Trans. Amer. Math. Soc. 371 (2019), 6341-6358
MSC (2010): Primary 14G05; Secondary 11G10
DOI: https://doi.org/10.1090/tran/7475
Published electronically: August 21, 2018
MathSciNet review: 3937327
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Abstract: 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$.


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Additional Information

Dragos Ghioca
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Email: dghioca@math.ubc.ca

Matthew Satriano
Affiliation: Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada
Email: msatriano@uwaterloo.ca

DOI: https://doi.org/10.1090/tran/7475
Received by editor(s): November 22, 2017
Published electronically: August 21, 2018
Additional Notes: The authors were partially supported by Discovery grants from the National Sciences and Engineering Research Council of Canada.
Article copyright: © Copyright 2018 American Mathematical Society