View in EDS HTML Full Text PDF Full Text

Reduction of Plane Quartics and Cayley Octads.

Saved in:
Bibliographic Details
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.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 194201082
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Reduction of Plane Quartics and Cayley Octads.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22van+Bommel%2C+Raymond%22">van Bommel, Raymond</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> r.vanbommel@bristol.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Docking%2C+Jordan%22">Docking, Jordan</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> jordan.docking.18@ucl.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Dokchitser%2C+Vladimir%22">Dokchitser, Vladimir</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> v.dokchitser@ucl.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Lercier%2C+Reynald%22">Lercier, Reynald</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> reynald.lercier@m4x.org</i><br /><searchLink fieldCode="AR" term="%22Lorenzo García%2C+Elisa%22">Lorenzo García, Elisa</searchLink><relatesTo>6,7</relatesTo> (AUTHOR)<i> elisa.lorenzo@unine.ch</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Foundations+of+Computational+Mathematics%22">Foundations of Computational Mathematics</searchLink>. Jun2026, Vol. 26 Issue 3, p1425-1496. 72p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Local+fields+%28Algebra%29%22">Local fields (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+curves%22">Algebraic curves</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+geometry%22">Algebraic geometry</searchLink><br /><searchLink fieldCode="DE" term="%22p-adic+analysis%22">p-adic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hyperelliptic+integrals%22">Hyperelliptic integrals</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>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.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=194201082
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10208-025-09704-y
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 72
        StartPage: 1425
    Subjects:
      – SubjectFull: Local fields (Algebra)
        Type: general
      – SubjectFull: Algebraic curves
        Type: general
      – SubjectFull: Algebraic geometry
        Type: general
      – SubjectFull: p-adic analysis
        Type: general
      – SubjectFull: Hyperelliptic integrals
        Type: general
    Titles:
      – TitleFull: Reduction of Plane Quartics and Cayley Octads.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: van Bommel, Raymond
      – PersonEntity:
          Name:
            NameFull: Docking, Jordan
      – PersonEntity:
          Name:
            NameFull: Dokchitser, Vladimir
      – PersonEntity:
          Name:
            NameFull: Lercier, Reynald
      – PersonEntity:
          Name:
            NameFull: Lorenzo García, Elisa
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 16153375
          Numbering:
            – Type: volume
              Value: 26
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Foundations of Computational Mathematics
              Type: main
ResultId 1