Conclusions.

It has been shown how to deal with polynomial system solving involving parameters, in the homogeneous case, by using as main tool the properties of Gröbner Bases under specialization. In conclusion, the most promising techniques are those based upon the using of the Hilbert function plus a simplification of the result ``á la GPT" and a future complete automatization of the algorithm already implemented will provide, in a very efficient way, a set of ``good specialization conditions" together with a Gröbner Basis of the considered homogeneous polynomial system for every one of those conditions.