Abstract
Let be the homogeneous ideal of a finite set Γ in of d points in linearly general position. In 1972, Saint-Donat proved that if then is generated by completely decomposable quadratic polynomials. Later, R. Treger generalized this result by showing that is generated by forms of degree if for some .
This paper aims to generalize Saint-Donat’s work in a different direction by proving that the degree m piece of can be generated by completely decomposable forms of degree m if and only if .
Communicated by Daniel Erman