On the moduli space of equilateral plane pentagons

Stephan Klaus; Sadayoshi Kojima

doi:10.1007/s13366-018-0429-z

On the moduli space of equilateral plane pentagons

Stephan Klaus^*, Sadayoshi Kojima

^*Corresponding author for this work

Global Center for Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 language	English
Pages (from-to)	487-497
Number of pages	11
Journal	Beitrage zur Algebra und Geometrie
Volume	60
Issue number	3
DOIs	https://doi.org/10.1007/s13366-018-0429-z
Publication status	Published - 2019 Sept 1

Keywords

Closed surface
Compactification
Moduli space
Pentagon
Rational parametrization

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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Cite this

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title = "On the moduli space of equilateral plane pentagons",

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.",

keywords = "Closed surface, Compactification, Moduli space, Pentagon, Rational parametrization",

author = "Stephan Klaus and Sadayoshi Kojima",

note = "Funding Information: The first author would like to thank Gert-Martin Greuel for his advice concerning real variable elimination and parametrization and to Dirk Siersma for helpful information and discussion on the non-equilateral case. The second author would like to thank Mathematisches Forschungsinstitut Oberwolfach where this work was started. Also he is partially supported by JSPS Grant no. 15H03619. ",

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AU - Kojima, Sadayoshi

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PY - 2019/9/1

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N2 - 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.

AB - 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.

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KW - Compactification

KW - Moduli space

KW - Pentagon

KW - Rational parametrization

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On the moduli space of equilateral plane pentagons

Abstract

Keywords

ASJC Scopus subject areas

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