In algebraic geometry

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 Plücker surface, studied by , 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....

 with a double line and 8 nodes.

Construction

For any quadric line complex, the lines of the complex in a plane envelop a quadric in the plane. A Plücker surface
depends on the choice of a quadric line complex and a line, and consists of points of the quadrics associated to the planes through the chosen line.