  Waring problem for homogeneus forms asks for additive decomposition of a form
$f$ into powers of linear forms. A classical problem is to determine when such
a decomposition is unique. In this paper I answer this question when the degree
of $f$ is greater than the number of variables. To do this I translate the
algebraic statement into a geometric one concerning the singularities of linear
systems of $P^n$ with assigned singularities.
