On positive bivariate quartic forms

TL;DR

This paper revisits the positivity criterion for bivariate quartic forms, reformulating it using pseudotensorial invariants to provide a potentially more elegant mathematical characterization.

Contribution

It introduces a reformulation of the positivity criterion for bivariate quartic forms using pseudotensorial invariants, enhancing the theoretical understanding.

Findings

Positivity criterion for bivariate quartic forms is expressed via pseudotensorial invariants.

The reformulation offers a new perspective on the structure of positive quartic forms.

The approach may facilitate further algebraic and geometric analysis of such forms.

Abstract

A bivariate quartic form is a homogeneous bivariate polynomial of degree four. A criterion of positivity for such a form is known. In the present paper this criterion is reformulated in terms of pseudotensorial invariants of the form.