Betti numbers of full Perazzo algebras

TL;DR

This paper investigates the algebraic structure of full Perazzo algebras, demonstrating they are doubles of 0-dimensional schemes and computing their Betti numbers, thus advancing understanding of their algebraic and geometric properties.

Contribution

It establishes that full Perazzo algebras are doubles of 0-dimensional schemes and provides explicit calculations of their minimal free resolutions.

Findings

Full Perazzo algebras are doubles of 0-dimensional schemes.

Computed graded Betti numbers of these algebras.

Enhanced understanding of their algebraic and geometric structure.

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 $n+1 = \binom{d+m-2}{m-1}$, 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 $A_F$.