Castelnuovo curve

In algebraic geometry, a Castelnuovo curve, studied by {{harvs|txt|last=Castelnuovo|authorlink=Guido Castelnuovo|year=1889}}, is a curve in projective space Pⁿ 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

:$g\backslash le\; (n-1)m(m-1)/2+m\backslash epsilon$

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.