Classification of Frobenius Forms in five variables

TL;DR

This paper classifies Frobenius forms, a special class of homogeneous polynomials, in up to five variables over algebraically closed fields of characteristic p>0, highlighting similarities with quadratic forms.

Contribution

It provides a complete classification of Frobenius forms in up to five variables, expanding understanding of their structure in positive characteristic.

Findings

Classification of Frobenius forms in five variables

Identification of similarities with quadratic forms

Insights into structure over algebraically closed fields

Abstract

We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.