Gorenstein algebras presented by quadrics

TL;DR

This paper investigates the structure of Gorenstein algebras with quadratic relations, establishing restrictions on their Hilbert functions and proposing conjectures supported by various algebraic techniques.

Contribution

It introduces new restrictions on Hilbert functions of quadratic Gorenstein algebras and presents conjectures with partial proofs using liaison theory and generic initial ideals.

Findings

Restrictions on Hilbert functions of quadratic Gorenstein algebras

Formulation of new conjectures in the area

Partial proofs supporting the conjectures

Abstract

We establish restrictions on the Hilbert function of standard graded Gorenstein algebras with only quadratic relations. Furthermore, we pose some intriguing conjectures and provide evidence for them by proving them in some cases using a number of different techniques, including liaison theory and generic initial ideals.