Reconstructing Plane Quartics from Their Invariants


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

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We would like to thank the participants of the working group TEDI, and in particular Boris Kolev and Marc Olive, for their interest and for the many useful discussions.

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Correspondence to Jeroen Sijsling.

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The first two authors acknowledge support from the CysMoLog “défi scientifique émergent” of the Université de Rennes 1.

Editor in Charge: János Pach

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Lercier, R., Ritzenthaler, C. & Sijsling, J. Reconstructing Plane Quartics from Their Invariants. Discrete Comput Geom 63, 73–113 (2020).

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  • Plane quartic curves
  • Invariant theory
  • Dixmier–Ohno invariants
  • Moduli spaces
  • Reconstruction

Mathematics Subject Classification

  • 13A50
  • 14L24
  • 14H10
  • 14H25