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Castelnuovo curve : ウィキペディア英語版
Castelnuovo curve
In algebraic geometry, a Castelnuovo curve, studied by , is a curve in projective space P''n'' of maximal genus ''g'' among irreducible non-degenerate curves of given degree ''d''.
Castelnuovo showed that the maximal genus is given by the Castelnuovo bound
:g\le (n-1)m(m-1)/2+m\epsilon
where ''m'' and ε are the quotient and remainder when dividing ''d''–1 by ''n''–1.
Castelnuovo described the curves satisfying this bound, showing in particular that they lie on either a rational normal scroll or on the Veronese surface.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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