Mathematical Research Letters

Volume 26 (2019)

Number 4

Bounding periods of subvarieties of $(\mathbb{P}^1)^n$

Pages: 949 – 971



Jason Bell (Department of Pure Mathematics, University of Waterloo, Ontario, Canada)

Dragos Ghioca (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)

Thomas J. Tucker (Department of Mathematics, University of Rochester, New York, U.S.A.)


Using methods of $p$-adic analysis, along with the powerful result of Medvedev and Scanlon [MS14] for the classification of periodic subvarieties of $(\mathbb{P}^1)^n$, we bound the length of the orbit of a periodic subvariety $Y \subset \mathbb{P}^1)^n$ under the action of a dominant endomorphism.

Received 7 December 2017

Accepted 5 July 2018

Published 25 October 2019