Stability of pencils of cubic surfaces P3

In this paper we study the classification of pencils of cubic surfaces in P3, up to projective equivalence. We obtain explicit vanishing criteria on the Plücker coordinates of a pencil for both stability and semi-stability; moreover, we give the equations defining pairs of generators for unstable and not properly stable pencils. Thus we extend the work of Miranda and Ballico [5, 1]. We give some geometric criteria for when a pencil is properly stable, and in particular, we give a characterization of smooth not properly stable pencils.Godkänd; 1999; 20070212 (evan)</p