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In mathematics, '''Wiman's sextic''' is a degree 6 [[plane curve]] with four [[Singular point of an algebraic variety|nodes]] studied by {{harvs|txt|last=Wiman|first=Anders|authorlink=Anders  Wiman |year=1896}}.
It is given by the equation (in [[homogeneous coordinates]])
:<math>x^6+y^6+z^6 + (x^2+y^2+z^2)(x^4+y^4+z^4)=12 x^2y^2z^2</math>
Its [[Normalization of an algebraic variety|normalization]] is a [[genus of an algebraic curve|genus]] 6 curve with [[automorphism group]] isomorphic to the [[symmetric group]] ''S''<sub>5</sub>.
 
==References==
 
*{{Citation | last1=Inoue | first1=Naoki | last2=Kato | first2=Fumiharu | title=On the geometry of Wiman's sextic | url=http://projecteuclid.org/euclid.kjm/1250281655 | id={{MR|2226628}} | year=2005 | journal=Journal of Mathematics of Kyoto University | issn=0023-608X | volume=45 | issue=4 | pages=743–757}}
*{{Citation | last1=Wiman | first1=A.|authorlink=Anders  Wiman | title=Zur Theorie der endlichen Gruppen von birationalen Transformationen in der Ebene | year=1896 | journal=[[Mathematische Annalen]] | volume=48 | pages=195–240 | doi=10.1007/BF01446342}}
 
[[Category:Algebraic curves]]

Revision as of 01:16, 30 January 2014

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

x6+y6+z6+(x2+y2+z2)(x4+y4+z4)=12x2y2z2

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

References

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