Geodesic
Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic
Igor Dolgachev1 ; JongHae Keum2
1 Department of Mathematics<br/>University of Michigan<br/>Ann Arbor, MI 48109<br/>United States
2 School of Mathematics<br/>Korea Institute for Advanced Study<br/>Seoul 130-722<br/>South Korea
Annals of mathematics, Tome 169 (2009) no. 1, pp. 269-313.

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We show that Mukai’s classification of finite 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 satisfied if $p > 11$. For $p=2,3,5,11$, we give examples of K3 surfaces with finite symplectic automorphism groups of order divisible by $p$ which are not contained in Mukai’s list.
DOI : 10.4007/annals.2009.169.269

Igor Dolgachev 1 ; JongHae Keum 2

1 Department of Mathematics<br/>University of Michigan<br/>Ann Arbor, MI 48109<br/>United States
2 School of Mathematics<br/>Korea Institute for Advanced Study<br/>Seoul 130-722<br/>South Korea 
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Igor Dolgachev; JongHae Keum. Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic. Annals of mathematics, Tome 169 (2009) no. 1, pp. 269-313. doi : 10.4007/annals.2009.169.269. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.269/

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