Quadratic equations of projective $PGL_2(\C)$-varieties

TL;DR

This paper explicitly describes the quadratic equations defining projective PGL_2(C)-varieties and explores their geometric properties, especially in relation to the Veronese curve.

Contribution

It provides explicit equations for PGL_2(C)-varieties defined by quadrics and analyzes their geometric structure and relation to the Veronese curve.

Findings

Explicit equations for PGL_2(C)-varieties are derived.

The zero-locus of these equations is characterized.

Connections with the geometry of the Veronese curve are established.

Abstract

We make explicit the equations of any projective $PGL_2(\C)$-variety defined by quadrics. We study their zero-locus and their relationship with the geometry of the Veronese curve.