Reduction of plane quartics and Dixmier–Ohno invariants: Reduction of plane quartics..

Raymond van Bommel; Jordan Docking; Reynald Lercier; Elisa Lorenzo García

doi:10.1007/s40993-024-00590-x

Reduction of plane quartics and Dixmier–Ohno invariants: Reduction of plane quartics..

Raymond van Bommel^*
, Jordan Docking
, Reynald Lercier
, Elisa Lorenzo García

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

Abstract

We characterise, in terms of Dixmier–Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.

Original language	English
Article number	41
Number of pages	25
Journal	Research in Number Theory
Volume	11
Issue number	1
Early online date	24 Feb 2025
DOIs	https://doi.org/10.1007/s40993-024-00590-x
Publication status	Published - 1 Mar 2025

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Keywords

Singularities
Invariants
Plane curves
Stable reduction

Access to Document

10.1007/s40993-024-00590-xLicence: CC BY

Handle.net

Persistent link

Cite this

@article{0adbacec9c1348509dc5ce9608ad1c9d,

title = "Reduction of plane quartics and Dixmier–Ohno invariants: Reduction of plane quartics..",

abstract = "We characterise, in terms of Dixmier–Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.",

keywords = "Singularities, Invariants, Plane curves, Stable reduction",

author = "\{van Bommel\}, Raymond and Jordan Docking and Reynald Lercier and Garc{\'i}a, \{Elisa Lorenzo\}",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = mar,

day = "1",

doi = "10.1007/s40993-024-00590-x",

language = "English",

volume = "11",

journal = "Research in Number Theory",

issn = "2363-9555",

publisher = "SpringerOpen",

number = "1",

}

TY - JOUR

T1 - Reduction of plane quartics and Dixmier–Ohno invariants

T2 - Reduction of plane quartics..

AU - van Bommel, Raymond

AU - Docking, Jordan

AU - Lercier, Reynald

AU - García, Elisa Lorenzo

PY - 2025/3/1

Y1 - 2025/3/1

N2 - We characterise, in terms of Dixmier–Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.

AB - We characterise, in terms of Dixmier–Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.

KW - Singularities

KW - Invariants

KW - Plane curves

KW - Stable reduction

U2 - 10.1007/s40993-024-00590-x

DO - 10.1007/s40993-024-00590-x

M3 - Article (Academic Journal)

SN - 2363-9555

VL - 11

JO - Research in Number Theory

JF - Research in Number Theory

IS - 1

M1 - 41

ER -

Reduction of plane quartics and Dixmier–Ohno invariants: Reduction of plane quartics..

Abstract

Bibliographical note

Keywords

Access to Document

Handle.net

Fingerprint

Cite this