Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic

By Igor Dolgachev, JongHae Keum. 2004

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We show that Mukai’s classication of nite groups which may act symplectically on a complex K3 surface extends to positive characteristic p under assumptions that (i) the order of the group is coprime to p and (ii) either the surface or its quotient is not birationally isomorphic to a supersingular K3 surface with Artin invariant 1. In the case without assumption (ii) we classify all possible new groups which may appear. We prove that assumption (i) on the order of the group is always satised if p > 11. For p = 2; 3; 5; 11, we give examples of K3 surfaces with nite symplectic automorphism groups of order divisible by p which are not contained in Mukai’s list.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b59e47bd744ce98b3bdf9e7268a5c48c8975b44