Reconstructing plane quartics from their invariants

TL;DR

This paper introduces an explicit method to reconstruct plane quartic curves from their Dixmier-Ohno invariants, enabling precise algebraic recovery of the curve from invariant data.

Contribution

The paper provides a novel explicit reconstruction technique for plane quartics from their invariants, advancing algebraic geometry and invariant theory.

Findings

Successful reconstruction of plane quartics from invariants

Explicit formulas for the reconstruction process

Potential applications in algebraic geometry and computational algebra

Abstract

We present an explicit method that, given a generic tuple of Dixmier-Ohno invariants, reconstructs a corresponding plane quartic curve.