Reconstructing plane quartics from their invariants

Abstract

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

36 pages

References in corpus (2)

• Plane quartics over $\mathbb{Q}$ with complex multiplication
• Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields

Cited by in corpus (3)

• Conductor and discriminant of Picard curves
• Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with $(\ell ,\ell ,\ell )$-isogenies
• The Dubrovin threefold of an algebraic curve