Symplectic automorphisms of prime order on K3 surfaces

Details Symplectic automorphisms of prime order on K3 surfaces Symplectic automorphisms of prime order on K3 surfaces

2006-03-31

arxiv.org/abs/math/0603742v2

J. of Algebra 318 (2007) 323-350

Mathematics

Algebraic Geometry

24 pages, final version

Scientific paper

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

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