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

  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, MR 1097176
This article is issued from Wikipedia - version of the Monday, April 08, 2013. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.