BELYI LATTÈS MAPS

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ZEYTİN A.

Kyushu Journal of Mathematics, vol.77, no.2, pp.221-235, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.2206/kyushujm.77.221
  • Journal Name: Kyushu Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.221-235
  • Keywords: absolute Galois group, Belyi maps, Lattès maps, Pick’s theorem
  • Galatasaray University Affiliated: Yes

Abstract

In this work, using elementary tools we determine those Lattès maps which are at the same time Belyi maps by explicitly determining their ramification data. It turns out that in the generic case, i.e. when the automorphism group is Z/2Z, the corresponding family of Lattès maps are Belyi maps if the isogeny is multiplication by two or four. Elliptic curves with extra automorphisms also determine families of Belyi maps. We provide examples of some Belyi Lattès maps together with a formula for such maps which may be used to write Belyi maps of arbitrarily high degree. We conclude the paper with a discussion of the field of definition of such Belyi pairs.