Bifurcations, intersections, and heights

Laura DeMarco*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for algebraic families of rational maps ft:ℙ1(ℂ) → ℙ1(ℂ), 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.

Original languageEnglish (US)
Pages (from-to)1031-1056
Number of pages26
JournalAlgebra and Number Theory
Volume10
Issue number5
DOIs
StatePublished - 2016

Keywords

  • Canonical height
  • Dynamics of rational maps
  • Stability

ASJC Scopus subject areas

  • Algebra and Number Theory

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