The stratification by automorphism groups of smooth plane sextic curves

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2025年2月15日

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Eslam Badr,
Francesc Bars

摘要

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.