Bommel, Raymond van;
Docking, Jordan;
Dokchitser, Vladimir;
Lercier, Reynald;
García, Elisa Lorenzo;
(2023)
Reduction of Plane Quartics and Cayley Octads.
arXiv.org: Ithaca, NY, USA.
Preview |
Text
Dokchitser_Reduction of Plane Quartics and Cayley Octads_Pre-print.pdf Download (6MB) | Preview |
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.
| Type: | Working / discussion paper |
|---|---|
| Title: | Reduction of Plane Quartics and Cayley Octads |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://discovery.ucl.ac.uk/id/eprint/10205747/1/O... |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10205747 |
Archive Staff Only
 |
View Item |
