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Ideal of the variety of flexes of plane cubics

Vladimir L. Popov

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.

Ideal of the variety of flexes of plane cubics

Abstract

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

Paper Structure

This paper contains 3 sections, 8 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Some properties of multi-cones
  3. Proof of Theorem \ref{['main']}

Key Result

Theorem 1

The ideal of $F$ is prime and generated by $f$ and $h$.

Theorems & Definitions (14)

  • Theorem 1
  • Corollary 1
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Corollary 2
  • proof
  • Lemma 2
  • proof
  • ...and 4 more