---
title: "Bibliography"
canonical: "https://docs.magma-maths.org/ArithmeticGeometry/PlaneQuartics/bibliography.html"
source: "https://docs.magma-maths.org/ArithmeticGeometry/PlaneQuartics/bibliography.md"
part: "Arithmetic Geometry"
chapter: "Plane Quartics"
breadcrumbs:
  - {"title": "Magma Handbook", "source": "../../index.md"}
  - {"title": "Arithmetic Geometry", "source": "../index-arithmetic-geometry.md"}
  - {"title": "Plane Quartics", "source": "index-plane-quartics.md"}
prev: {"title": "Twists", "source": "quartic_twists.md"}
next: {"title": "Hyperelliptic Curves", "source": "../HyperellipticCurves/index-hyperelliptic-curves.md"}
---

# Bibliography

<a id="cite-buse14"></a>
- **[BJ14]** Laurent Busé and Jean-Pierre Jouanolou. On the discriminant scheme of homogeneous polynomials. *Math. Comput. Sci.*, 8(2):175–234, 2014.
<a id="cite-dixmier87"></a>
- **[Dix87]** J. Dixmier. On the projective invariants of quartic plane curves. *Adv. in Math.*, 64:279–304, 1987.
<a id="cite-elsenhans15"></a>
- **[Els15]** Andreas-Stephan Elsenhans. Explicit computations of invariants of plane quartic curves. *J. Symbolic Comput.*, 68(part 2):109–115, 2015.
<a id="cite-giko06"></a>
- **[GK06]** M. Girard and D. R. Kohel. Classification of genus 3 curves in special strata of the moduli space. In Hess, F. (ed.) et al., Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23–28, 2006. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 4076, 346-360 (2006)., 2006.
<a id="cite-lllr20"></a>
- **[LLGR20]** Reynald Lercier, Qing Liu, Elisa Lorenzo García, and Christophe Ritzenthaler. Reduction type of smooth quartics. 2020. [arXiv:1803.05816](https://arxiv.org/abs/1803.05816).
<a id="cite-lrrs14"></a>
- **[LRRS14]** Reynald Lercier, Christophe Ritzenthaler, Florent Rovetta, and Jeroen Sijsling. Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields. *LMS J. Comput. Math.*, 17(suppl. A):128–147, 2014.
<a id="cite-lerisi16"></a>
- **[LRS16]** Reynald Lercier, Christophe Ritzenthaler, and Jeroen Sijsling. Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group. *Math. Comp.*, 85(300):2011–2045, 2016.
<a id="cite-meto10"></a>
- **[MT10]** Stephen Meagher and Jaap Top. Twists of genus three curves over finite fields. *Finite Fields Appl.*, 16(5):347–368, 2010.
<a id="cite-ohno07"></a>
- **[Ohn07]** T. Ohno. The graded ring of invariants of ternary quartics I. 2007. Unpublished.
<a id="cite-salmon79"></a>
- **[Sal79]** G. Salmon. *A Treatise on the Higher Plane Curves*. Hodges, Foster and Co, Dublin, 3rd edition, 1879.
<a id="cite-vanrijnswou01"></a>
- **[vR01]** Sander Matthijs van Rijnswou. *Testing the equivalence of planar curves*. PhD thesis, Technische Universiteit Eindhoven, Eindhoven, 2001.
<a id="cite-lrs18"></a>
- **[LRS18]** R. Lercier, C. Ritzenthaler, and J. Sijsling. Reconstructing plane quartics from their invariants. *Discrete & Computational Geometry*, pages 1–41, 2018.