On completely decomposable defining equations of finite sets in P<SUP>n</SUP>

초록

Let I(Gamma) be the homogeneous ideal of a finite set l' in P-n of d points in linearly general position. In 1972, Saint-Donat proved that if d <= 2n then I(Gamma) is generated by completely decomposable quadratic polynomials. Later, R. Treger generalized this result by showing that I(Gamma) is generated by forms of degree <= m if d <= mn for some m >= 2. This paper aims to generalize Saint-Donat's work in a different direction by proving that the degree m piece of I(Gamma) can be generated by completely decomposable forms of degree m if and only if d <= mn.

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