Wiman's sextic

In mathematics, Wiman's sextic is a degree 6 plane curve with four nodes studied by Anders Wiman (1896). It is given by the equation (in homogeneous coordinates)

${\displaystyle x^{6}+y^{6}+z^{6}+(x^{2}+y^{2}+z^{2})(x^{4}+y^{4}+z^{4})=12x^{2}y^{2}z^{2}}$

Its normalization is a genus 6 curve with automorphism group isomorphic to the symmetric group S₅.

References

• Inoue, Naoki; Kato, Fumiharu (2005), "On the geometry of Wiman's sextic", Journal of Mathematics of Kyoto University, 45 (4): 743–757, doi:10.1215/kjm/1250281655, ISSN 0023-608X, MR 2226628
• Wiman, A. (1896), "Zur Theorie der endlichen Gruppen von birationalen Transformationen in der Ebene", Mathematische Annalen, 48 (1–2): 195–240, doi:10.1007/BF01446342, S2CID 123516972