Reduction of Plane Quartics and Cayley Octads
Abstract We give a conjectural characterisation of the stable reduction of plane quartics over local fields in terms of their Cayley octads. This results in p -adic criteria that efficiently give the stable reduction type amongst the 42 possible types, and whether the reduction is hyperelliptic or not. These criteria are in the vein of the machinery of “cluster pictures” for hyperelliptic curves. We also construct explicit families of quartic curves that realise all possible stable types, against which we test these criteria. We give numerical examples that illustrate how to use these criteria in practice.
Authors
- Elisa Lorenzo García (ORCID: https://orcid.org/0000-0001-7360-1411)
- Jordan Docking (ORCID: https://orcid.org/0009-0000-1646-2785)
- Vladimir Dokchitser (ORCID: https://orcid.org/0000-0003-4384-4193)
- Raymond van Bommel (ORCID: https://orcid.org/0000-0003-3767-1740)
- Reynald Lercier
Institutions
- Centre National de la Recherche Scientifique (FR)
- University of Bristol (GB)
- Institut de recherche mathématique de Rennes (FR)
- University College London (GB)
- Université de Rennes (FR)
- University of Neuchâtel (CH)
- Massachusetts Institute of Technology (US)
Publication Details
- Journal
- Foundations of Computational Mathematics
- Published
- 2025-06-02
- DOI
- https://doi.org/10.1007/s10208-025-09704-y
- Citations
- 3
- Primary Topic
- Finite Group Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 15.99
Funders
- Centre Henri Lebesgue
- University College London
- Agence Nationale de la Recherche
- Engineering and Physical Sciences Research Council