# A strategy and a new operator to generate covariants in small characteristic

## TL;DR

This paper introduces a novel method for constructing covariants in small characteristic fields, including a new operator and a separating system for binary quartics in characteristic 3, advancing invariant theory in these settings.

## Contribution

It presents a new approach to generate covariants in small characteristic and introduces a new operator, with specific applications to binary quartics in characteristic 3.

## Key findings

- Constructed covariants using a Sturmfels-like approach
- Developed a new operator for covariants in small characteristic
- Found a separating system for binary quartic in characteristic 3

## Abstract

We present some new results about covariants in small characteristic. In section 1, we give a method to construct covariants using an approach similar to Sturmfels. We apply our method to find a separating system of covariants for binary quartic in characteristic 3. In the second section, we construct a new operator on covariants when the characteristic is small compared to the degree of the form.