Reduction of Plane Quartics and Cayley Octads
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10208_2025_Article_9704.pdf
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2.97 MB
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2eadb94a5a93ab34b6383e481c8be387
Author(s)
van Bommel, Raymond
Docking, Jordan
Dokchitser, Vladimir
Lercier, Reynald
Lorenzo García, Elisa
Date Issued
June 2, 2025
Journal
Foundations of Computational Mathematics
Publisher
Springer US
Citation
van Bommel, R., Docking, J., Dokchitser, V. et al. Reduction of Plane Quartics and Cayley Octads. Found Comput Math (2025).
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s10208-025-09704-y
