The stratification by automorphism groups of smooth plane sextic curves
Abstract We obtain the list of automorphism groups for smooth plane sextic curves over an algebraically closed field K of characteristic $$p=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> or $$p>21$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>21</mml:mn> </mml:mrow> </mml:math> . Moreover, we assign to each group a geometrically complete family over K that describe the corresponding stratum, that is, a generic polynomial equation with parameters such that any curve in the stratum is K -isomorphic to a smooth plane model obtained by specializing the values of those parameters in K . Additionally, we explore the connection with K3 surfaces of degree 2.
Authors
- Francesc Bars (ORCID: https://orcid.org/0000-0003-4779-3995)
- Eslam Badr (ORCID: https://orcid.org/0000-0002-3960-7243)
Institutions
- Universitat Autònoma de Barcelona (ES)
- Cairo University (EG)
- Centre de Recerca Matemàtica (ES)
- American University in Cairo (EG)
Publication Details
- Journal
- Annali di Matematica Pura ed Applicata (1923 -)
- Published
- 2025-02-15
- DOI
- https://doi.org/10.1007/s10231-025-01558-z
- Citations
- 1
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- American University in Cairo
- Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España
- Universitat Autònoma de Barcelona
- Agencia Estatal de Investigación