Plücker surface
{{For|the hypersurface parameterizing lines in 3-space, also sometimes called a Plücker surface|Plücker coordinates}}
In algebraic geometry, a Plücker surface, studied by {{harvs|txt|authorlink=Julius Plücker|first=Julius |last=Plücker|year=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.{{Citation | authorlink=R. W. H. T. Hudson | last1=Hudson | first1=R. W. H. T. | title=Kummer's quartic surface | page=68 | publisher=Cambridge University Press | series=Cambridge Mathematical Library | isbn=978-0-521-39790-2 | mr=1097176 | year=1990|url=https://archive.org/details/184605691}}
References
{{Reflist}}
- {{Citation | last1=Jessop | first1=C. M. | title=Quartic surfaces with singular points | url=http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=04290002 | publisher=Cornell University Library | isbn=978-1-4297-0393-2 | year=1916}}
- {{Citation | last1=Miles | first1=Henry J. | title=On a Generalization of Plucker's Surface | jstor=1968230 | publisher=Annals of Mathematics | series=Second Series | year=1930 | journal=Annals of Mathematics | issn=0003-486X | volume=31 | issue=3 | pages=355–365 | doi=10.2307/1968230}}
- {{Citation | last1=Plücker | first1=Julius | title=Neue Geometrie des Raumes, gegründet auf die Betrachtung der geraden Linie als Raumelement. | url=https://archive.org/details/neuegeoraum00plucrich | publisher=University of Michigan Library | isbn=978-1-4181-6773-8 | year=1869}}
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