Moduli spaces of quadratic rational maps with a marked periodic point of small order

Blanc, Jérémy and Canci, Jung-Kyu 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. 12459-12489.

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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 > Algebraische Geometrie (Blanc)
UniBasel Contributors:Blanc, Jérémy and Canci, Jung Kyu
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Oxford University Press
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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