Plücker surface

Short description: Algebraic geometry surface, studied by Julius Plücker (1899)

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

1. ↑ Hudson, R. W. H. T. (1990), Kummer's quartic surface, Cambridge Mathematical Library, Cambridge University Press, p. 68, ISBN 978-0-521-39790-2, https://archive.org/details/184605691

* Jessop, C. M. (1916), Quartic surfaces with singular points, Cornell University Library, ISBN 978-1-4297-0393-2, https://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=04290002
* 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
* Plücker, Julius (1869), Neue Geometrie des Raumes, gegründet auf die Betrachtung der geraden Linie als Raumelement., University of Michigan Library, ISBN 978-1-4181-6773-8, https://archive.org/details/neuegeoraum00plucrich

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