Editing Kummer surface (section)

{{short description|Irreducible nodal surface}}
[[Image:Kummer surface.png|right|400px|Plot of the real points]]
[[File:3D model of a Kummer surface.stl|thumb|3D model of a Kummer surface]]

In [[algebraic geometry]], a '''Kummer quartic surface''', first studied by {{harvs|txt|first=Ernst|last=Kummer|authorlink=Ernst Kummer|year=1864}}, is an [[irreducible space|irreducible]] [[nodal surface]] of degree 4 in [[Projective_space#Definition_of_projective_space|<math>\mathbb{P}^3</math>]]  with the maximal possible number of 16 double points. Any such surface is the [[Kummer variety]] of the [[Jacobian variety]] of a smooth [[hyperelliptic curve]] of [[genus (mathematics)|genus]] 2; i.e. a quotient of the Jacobian by the Kummer involution ''x''&nbsp;↦&nbsp;&minus;''x''. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. 
Resolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a [[K3 surface]] with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces.

Other surfaces closely related to Kummer surfaces include [[Weddle surface]]s, [[wave surface]]s, and [[tetrahedroid]]s.