Multiplier spectra and the moduli space of degree 3 morphisms on ℙ1

Benjamin Hutz, Michael Louis Tepper

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The moduli space of degree d morphisms on ℙ1 has received much study. McMullen showed that, except for certain families of Lattès maps, there is a finite-to-one correspondence (over ℂ) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms, Milnor (over ℂ) and Silverman (over ℤ) showed that the correspondence is an isomorphism [8, 10]. In this article, we address two cases with algebraic methods: polynomial maps of any degree and rational maps of degree 3.

Original languageEnglish (US)
Pages (from-to)189-206
Number of pages18
JournalJP Journal of Algebra, Number Theory and Applications
Volume29
Issue number2
StatePublished - 2013

Fingerprint

Morphisms
Moduli Space
Multiplier
Correspondence
Polynomial Maps
Rational Maps
Algebraic Methods
Periodic Points
Isomorphism

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

@article{c82b145e8d714b608ddcb11562ce31b7,
title = "Multiplier spectra and the moduli space of degree 3 morphisms on ℙ1",
abstract = "The moduli space of degree d morphisms on ℙ1 has received much study. McMullen showed that, except for certain families of Latt{\`e}s maps, there is a finite-to-one correspondence (over ℂ) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms, Milnor (over ℂ) and Silverman (over ℤ) showed that the correspondence is an isomorphism [8, 10]. In this article, we address two cases with algebraic methods: polynomial maps of any degree and rational maps of degree 3.",
author = "Benjamin Hutz and Tepper, {Michael Louis}",
year = "2013",
language = "English (US)",
volume = "29",
pages = "189--206",
journal = "JP Journal of Algebra, Number Theory and Applications",
issn = "0972-5555",
publisher = "Pushpa Publishing House",
number = "2",

}

Multiplier spectra and the moduli space of degree 3 morphisms on ℙ1. / Hutz, Benjamin; Tepper, Michael Louis.

In: JP Journal of Algebra, Number Theory and Applications, Vol. 29, No. 2, 2013, p. 189-206.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Multiplier spectra and the moduli space of degree 3 morphisms on ℙ1

AU - Hutz, Benjamin

AU - Tepper, Michael Louis

PY - 2013

Y1 - 2013

N2 - The moduli space of degree d morphisms on ℙ1 has received much study. McMullen showed that, except for certain families of Lattès maps, there is a finite-to-one correspondence (over ℂ) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms, Milnor (over ℂ) and Silverman (over ℤ) showed that the correspondence is an isomorphism [8, 10]. In this article, we address two cases with algebraic methods: polynomial maps of any degree and rational maps of degree 3.

AB - The moduli space of degree d morphisms on ℙ1 has received much study. McMullen showed that, except for certain families of Lattès maps, there is a finite-to-one correspondence (over ℂ) between classes of morphisms in the moduli space and the multipliers of the periodic points. For degree 2 morphisms, Milnor (over ℂ) and Silverman (over ℤ) showed that the correspondence is an isomorphism [8, 10]. In this article, we address two cases with algebraic methods: polynomial maps of any degree and rational maps of degree 3.

UR - http://www.scopus.com/inward/record.url?scp=84880488438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880488438&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84880488438

VL - 29

SP - 189

EP - 206

JO - JP Journal of Algebra, Number Theory and Applications

JF - JP Journal of Algebra, Number Theory and Applications

SN - 0972-5555

IS - 2

ER -