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In [[algebraic geometry]], a '''White surface''' is one of the [[rational surface]]s in ''P''<sup>''n''</sup> studied by {{harvtxt|White|1923}}, generalizing [[cubic surface]]s and [[Bordiga surface]]s which are the cases ''n'' = 3 or&nbsp;4.
In [[algebraic geometry]], a '''White surface''' is one of the [[rational surface]]s in ''P''<sup>''n''</sup> studied by {{harvtxt|White|1923}}, generalizing [[cubic surface]]s and [[Bordiga surface]]s, which are the cases ''n'' = 3 or&nbsp;4.


A White surface in ''P''<sup>''n''</sup> is given by the embedding of ''P''<sup>2</sup> [[blowing up|blown up]] in ''n''(''n''&nbsp;+&nbsp;1)/2 points by the linear system of degree ''n'' curves through these points.
A White surface in ''P''<sup>''n''</sup> is given by the embedding of ''P''<sup>2</sup> [[blowing up|blown up]] in ''n''(''n''&nbsp;+&nbsp;1)/2 points by the linear system of degree ''n'' curves through these points.


==References==
==References==
*{{citation|first=F. P. |last=White|title=On certain nets of plane curves|journal=Proceedings of the Cambridge philosophical society|volume=22|year=1923|pages=1&ndash;10}}
*{{citation|first=F. P. |last=White|title=On certain nets of plane curves|journal=Proceedings of the Cambridge Philosophical Society|volume=22|year=1923|pages=1&ndash;10|doi=10.1017/S0305004100000037}}


[[Category:complex surfaces]]
[[Category:Complex surfaces]]
[[Category:algebraic surfaces]]
[[Category:Algebraic surfaces]]

Latest revision as of 22:20, 25 March 2018

In algebraic geometry, a White surface is one of the rational surfaces in Pn studied by White (1923), generalizing cubic surfaces and Bordiga surfaces, which are the cases n = 3 or 4.

A White surface in Pn is given by the embedding of P2 blown up in n(n + 1)/2 points by the linear system of degree n curves through these points.

References

[edit]
  • White, F. P. (1923), "On certain nets of plane curves", Proceedings of the Cambridge Philosophical Society, 22: 1–10, doi:10.1017/S0305004100000037