Cohomological dimension and cubic surfaces

In this thesis we give necessary and sufficient conditions for a curve C on a given cubic surface Q so that Q − C is affine. We use this to give a simpler proof of cd(P 3 − C) = 1 by using Budach’s method for these curves.We investigate the nature of curves on cubic surfaces such that the cubic surface minus these curves is an affine variety. We give combinatorial conditions for the existence of such curves.