Translator Disclaimer
2016 Bifurcations, intersections, and heights
Laura DeMarco
Algebra Number Theory 10(5): 1031-1056 (2016). DOI: 10.2140/ant.2016.10.1031

Abstract

We prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps ft : 1() 1(), parameterized by t in a quasiprojective complex variety. We use this to prove one implication in the if-and-only-if statement of a certain conjecture on unlikely intersections in the moduli space of rational maps (see “Special curves and postcritically finite polynomials”, Forum Math. Pi 1 (2013), e3). We present the conjecture here in a more general form.

Citation

Download Citation

Laura DeMarco. "Bifurcations, intersections, and heights." Algebra Number Theory 10 (5) 1031 - 1056, 2016. https://doi.org/10.2140/ant.2016.10.1031

Information

Received: 16 June 2015; Revised: 10 February 2016; Accepted: 10 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06617178
MathSciNet: MR3531361
Digital Object Identifier: 10.2140/ant.2016.10.1031

Subjects:
Primary: 37P30
Secondary: 11G05, 37F45

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.10 • No. 5 • 2016
MSP
Back to Top