Reduction of Plane Quartics and Cayley Octads.
Saved in:
| Title: | Reduction of Plane Quartics and Cayley Octads. |
|---|---|
| Authors: | van Bommel, Raymond1,2 (AUTHOR) r.vanbommel@bristol.ac.uk, Docking, Jordan3 (AUTHOR) jordan.docking.18@ucl.ac.uk, Dokchitser, Vladimir4 (AUTHOR) v.dokchitser@ucl.ac.uk, Lercier, Reynald5 (AUTHOR) reynald.lercier@m4x.org, Lorenzo García, Elisa6,7 (AUTHOR) elisa.lorenzo@unine.ch |
| Source: | Foundations of Computational Mathematics. Jun2026, Vol. 26 Issue 3, p1425-1496. 72p. |
| Subjects: | Local fields (Algebra), Algebraic curves, Algebraic geometry, p-adic analysis, Hyperelliptic integrals |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Foundations of Computational Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
|
Full text is not displayed to guests.
Login for full access.
|
|
| 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. [ABSTRACT FROM AUTHOR] |
|---|---|
| ISSN: | 16153375 |
| DOI: | 10.1007/s10208-025-09704-y |
