@article{2316b35ea6624314bccd6f7bd8cc01b8,
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. ",
year = "2019",
month = sep,
day = "1",
doi = "10.1007/s13366-018-0429-z",
language = "English",
volume = "60",
pages = "487--497",
journal = "Beitrage zur Algebra und Geometrie",
issn = "0138-4821",
publisher = "Springer Berlin",
number = "3",
}