Ideal of the variety of flexes of plane cubics

TL;DR

This paper proves that the variety of flexes of plane cubic curves forms a complete intersection ideal in a specific product of projective spaces, providing a precise algebraic geometric characterization.

Contribution

It establishes that the variety of flexes of degree 3 algebraic curves is a complete intersection ideal in a product of projective spaces, a novel algebraic geometric result.

Findings

The variety of flexes is a complete intersection ideal.

The variety is embedded in a product of a 2D and 9D projective space.

Provides an explicit algebraic geometric description.

Abstract

We prove that the variety of flexes of algebraic curves of degree $3$ in the projective plane is an ideal theoretic complete intersection in the product of a two-dimensional and a nine-dimensional projective spaces.