Work

The stratification by automorphism groups of smooth plane sextic curves

Year: 2025

Type: article

Abstract: We obtain the list of automorphism groups for smooth plane sextic curves over an algebraically closed field K of characteristic $$p=0$$ p = 0 or $$p>21$$ p > 21 . 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.

Source: Annali di Matematica Pura ed Applicata (1923 -)

DOI: 10.1007/s10231-025-01558-z

Authors: Eslam Badr, Francesc Bars

Institutions: Cairo University, American University in Cairo, Universitat Autònoma de Barcelona, Centre de Recerca Matemàtica

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: American University in Cairo, Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España, Universitat Autònoma de Barcelona, Agencia Estatal de Investigación