A note on the j invariant and foliations

TL;DR

This paper explores the geometry of Veronese curves and classical invariant theory to analyze the exceptional component of integrable forms of degree two, providing new insights into the structure of these mathematical objects.

Contribution

It offers a geometric and invariant-theoretic analysis of the exceptional component of integrable degree-two forms, linking it to Veronese curves.

Findings

Characterization of the exceptional component via Veronese curves

Connection established between invariant theory and integrable forms

New geometric insights into the structure of integrable forms

Abstract

In this note we analyse the Exceptional Component of the space of integrable forms of degree two, introduced by Cerveau-Lins Neto, in terms of the geometry of Veronese curves and classical invariant theory.