Hesse Pencils and 3-Torsion Structures

TL;DR

This paper explores the universal properties of Hesse pencils and their twists, providing explicit and elementary descriptions applicable in all characteristics except three.

Contribution

It offers a clear, elementary treatment of the universal property of Hesse pencils and their twists, extending applicability across various characteristics.

Findings

Explicit description of the universal property of Hesse pencils

Elementary approach applicable in all characteristics except three

Extension of properties to twists of Hesse pencils

Abstract

This paper intends to focus on the universal property of this Hesse pencil and of its twists. The main goal is to do this as explicit and elementary as possible, and moreover to do it in such a way that it works in every characteristic different from three.