On the moduli space of equilateral plane pentagons

Stephan Klaus, Sadayoshi Kojima

Research output: Contribution to journalArticle

Abstract

We give two new proofs of the well-known result that the moduli space M5 of equilateral plane pentagons is a closed surface of genus four. Moreover, we construct a new algebraic description of this space, also in the non-equilateral case, as a real affine algebraic surface F defined by a polynomial p(x, y, z) of degree 12. This allows a visualization using the Surfer software.

Original languageEnglish
Pages (from-to)487-497
Number of pages11
JournalBeitrage zur Algebra und Geometrie
Volume60
Issue number3
DOIs
Publication statusPublished - 2019 Sep 1

Fingerprint

Equilateral
Pentagon
Algebraic Surfaces
Moduli Space
Genus
Visualization
Closed
Polynomial
Software

Keywords

  • Closed surface
  • Compactification
  • Moduli space
  • Pentagon
  • Rational parametrization

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

On the moduli space of equilateral plane pentagons. / Klaus, Stephan; Kojima, Sadayoshi.

In: Beitrage zur Algebra und Geometrie, Vol. 60, No. 3, 01.09.2019, p. 487-497.

Research output: Contribution to journalArticle

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