Mathematical plane curve
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 )
x
6
+
y
6
+
z
6
+
(
x
2
+
y
2
+
z
2
)
(
x
4
+
y
4
+
z
4
)
=
12
x
2
y
2
z
2
{\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 S 5 .
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 Category :
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
**DISCLAIMER** We are not affiliated with Wikipedia, and Cloudflare.
The information presented on this site is for general informational purposes only and does not constitute medical advice.
You should always have a personal consultation with a healthcare professional before making changes to your diet, medication, or exercise routine.
AI helps with the correspondence in our chat.
We participate in an affiliate program. If you buy something through a link, we may earn a commission 💕
↑
