Castelnuovo curve
# Castelnuovo curve

In algebraic geometry, a Castelnuovo curve, studied by Castelnuovo (1889), 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

    $g\leq (n-1)m(m-1)/2+m\epsilon$

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.

