Weddle surface
Encyclopedia
In algebraic geometry
, a Weddle surface is a quartic surface
in 3-dimensional projective space
, given by the locus of vertices of the 3-dimensional family of cones passing through 6 points in general position
, and studied by .
Weddle surfaces have 6 nodes and are birational to Kummer surfaces.
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, a Weddle surface is a quartic surface
Quartic surface
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4.More specifically there are two closely related types of quartic surface: affine and projective...
in 3-dimensional projective space
Projective space
In mathematics a projective space is a set of elements similar to the set P of lines through the origin of a vector space V. The cases when V=R2 or V=R3 are the projective line and the projective plane, respectively....
, given by the locus of vertices of the 3-dimensional family of cones passing through 6 points in general position
General position
In algebraic geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible...
, and studied by .
Weddle surfaces have 6 nodes and are birational to Kummer surfaces.