  Let X be a regular irreducible variety in CP^{n-1}, Y the associated
homogeneous variety in C^n, and N the restriction of the universal bundle of
CP^{n-1} to X. In the present paper, we compute the obstructions to solving the
d-bar-equation in the L^p-sense on Y for 1<=p<=\infty in terms of cohomology
groups H^q(X,O(N^m)). That allows to identify obstructions explicitly if X is
specified more precisely, for example if it is equivalent to CP^1 or an
elliptic curve.
