Plane rational quartics and K3 surfaces


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Аннотация

We study actions of the symmetric group S4 on K3 surfaces X that satisfy the following condition: there exists an equivariant birational contraction \(\bar r:X \to \bar X\) to a K3 surface \(\bar X\) with ADE singularities such that the quotient space \(\bar X\)/S4 is isomorphic to P2. We prove that up to smooth equivariant deformations there exist exactly 15 such actions of the group S4 on K3 surfaces, and that these actions are realized as actions of the Galois groups on the Galoisations \(\bar X\) of the dualizing coverings of the plane which are associated with plane rational quartics without A4, A6, and E6 singularities as their singular points.

Авторлар туралы

Vik. Kulikov

Steklov Mathematical Institute of Russian Academy of Sciences

Хат алмасуға жауапты Автор.
Email: kulikov@mi.ras.ru
Ресей, ul. Gubkina 8, Moscow, 119991

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