Classification of Tor algebras for rings from general points by Waring Rank

Abstract

We determine the multiplicative structure on the Tor algebras associated to the coordinate rings of general points in ${\mathbb{P}}^3$ in terms of the number of points. We show that in codimension four, the Waring rank of a form determines the Tor algebra class of its apolar Artinian Gorenstein ring for a dense subset of the forms of fixed Waring rank and sufficiently large degree.