Betti numbers of full Perazzo algebras

Abstract

In this paper we prove that any full Perazzo algebra $A_F$, whose Macaulay dual generator is a Perazzo form $F\in K[X_0,\dots ,X_n,U_1,\dots ,U_m{]}_d$ with $n+1=\left(\genfrac{}{}{0ex}{}{d+m-2}{m-1}\right)$, is the doubling of a 0-dimensional scheme in $\PP^{n+m}$ and we compute the graded Betti numbers of a minimal free resolution of $A_F$.

To be published in Annali di Matematica Pura ed Applicata