Galois coverings of the plane by K3 surfaces

Abstract

We study branched Galois coverings of the projective plane by smooth K3 surfaces. Branching data of such a covering determines in a unique way a uniformizable orbifold on the plane. In order to study Galois coverings of the plane by K3 surfaces, it suffices to study orbifolds on the plane uniformized by K3 surfaces. We call these K3 orbifolds and classify K3 orbifolds with an abelian uniformization. We also classify K3 orbifolds with a locus of degree less than 6 and with a non-abelian uniformization. There are no K3 orbifolds with a locus of degree greater than 6. Although we give some examples of K3 orbifolds with a sextic locus, our results are incomplete in this case. © 2005, Faculty of Mathematics, Kyushu University. All rights reserved.