Space curves with the expected postulation

Abstract

AbstractThe postulation of a space curve is a classifying invariant which computes for any integer n the dimension of the family of surfaces of degree n containing the curve. We prove that for any integers d and g satisfying d−3⩽g⩽2d−9, there exists a smooth connected curve of degree d and genus g with the minimal postulation expected by the Riemann–Roch theorem