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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 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 4. |
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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'' + 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'' + 1)/2 points by the linear system of degree ''n'' curves through these points. |
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==References== |
==References== |
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*{{citation|first=F. P. |last=White|title=On certain nets of plane curves|journal=Proceedings of the Cambridge |
*{{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=1–10|doi=10.1017/S0305004100000037}} |
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[[Category: |
[[Category:Complex surfaces]] |
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[[Category: |
[[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