In
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, a Plücker surface, studied by , is a
quartic surface in 3-dimensional
projective space
In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet ''at infinity''. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally ...
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.
References
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{{DEFAULTSORT:Plucker Surface
Algebraic surfaces