Plücker surface

For the hypersurface parameterizing lines in 3-space, also sometimes called a Plücker surface, see Plücker coordinates.

In algebraic geometry, a Plücker surface, studied by Julius Plücker (1899), is a quartic surface in 3-dimensional projective space 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.^[1]

References

↑ Hudson, R. W. H. T. (1990), Kummer's quartic surface, Cambridge Mathematical Library, Cambridge University Press, p. 68, ISBN 978-0-521-39790-2, MR 1097176

Jessop, C. M. (1916), Quartic surfaces with singular points, Cornell University Library, ISBN 978-1-4297-0393-2
Miles, Henry J. (1930), "On a Generalization of Plucker's Surface", Annals of Mathematics, Second Series (Annals of Mathematics) 31 (3): 355–365, doi:10.2307/1968230, ISSN 0003-486X, JSTOR 1968230
Plücker, Julius (1899), Neue geometrie des raumes gegründet auf die betrachtung der geraden linie als raumelement., University of Michigan Library, ISBN 978-1-4181-6773-8