Blanc, Jérémy and Canci, JungKyu and Elkies, Noam D.. (2015) Moduli spaces of quadratic rational maps with a marked periodic point of small order. International mathematics research notices, 2015 (23). pp. 1245912489.
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Official URL: http://edoc.unibas.ch/39401/
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Abstract
The surface corresponding to the moduli space of quadratic endomorphisms of P1 with a marked periodic point of order n is studied. It is shown that the surface is rational over Q when n 5 and is of general type for n = 6. An explicit description of the n = 6 surface lets us find several infinite families of quadratic endomorphisms f : P1> P1 defined over Q with a rational periodic point of order 6. In one of these families, f also has a rational fixed point, for a total of at least 7 periodic and 7 preperiodic points. This is in contrast with the polynomial case, where it is conjectured that no polynomial endomorphism defined over Q admits rational periodic points of order n > 3.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc) 

UniBasel Contributors:  Blanc, Jérémy and Canci, Jung Kyu 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  Oxford University Press 
ISSN:  10737928 
Note:  Publication type according to Uni Basel Research Database: Journal article 
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Last Modified:  30 Jun 2016 10:59 
Deposited On:  03 May 2016 09:30 
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