In algebraic geometry, a Castelnuovo curve, studied by , is a curve in projective space P<sup>n</sup> 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
where m and õ are the quotient and remainder when dividing dâÂÂ1 by nâÂÂ1. Castelnuovo described the curves satisfying this bound, showing in particular that they lie on either a rational normal scroll or on the Veronese surface.