No abstract

Abstract.F. S. Macaulay gave necessary and sufficient conditions on the growth of a nonnegative integer-valued function which determine when such a function can be the Hubert function of a standard graded A:-algebra. We investigate some algebraic and geometric consequences which arise from the extremal cases of Macaulay's theorem. Our work also builds on the fundamental work of G. Gotzmann.Our principal applications are to the study of Hubert functions of zeroschemes with uniformity conditions. As a consequence, we have new strong limitations on the possible Hubert functions of the points which arise as a general hyperplane section of an irreducible curve.

In this paper we compute the Waring rank of any polynomial of\ud the form F=M1+...+Mr, where the Mi are pairwise\ud coprime monomials, i.e., GCD(Mi, Mj)=1 for i different from j. In\ud particular, we determine the Waring rank of any monomial. As an\ud application we show that certain monomials in three variables give examples of forms of rank higher than the generic form. As a further\ud application we produce a sum of power decomposition for any form\ud which is the sum of pairwise coprime monomials

No abstract