ON THE COHOMOLOGY OF A SPACE CURVE CONTAINING A PLANE CURVE

Abstract

In this paper we study the Hartshorne–Rao module of curves in P 3 of degree d and genus g, containing plane curves of degree d − p, p ≥ 1. We prove an optimal upper bound for the Rao function of these curves and we show that the curves attaining the bound are obtained from an extremal curve by an elementary biliaison of height min(p, d − p) − 1 on a quadric surface.