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
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.