6533b85dfe1ef96bd12bf25e

RESEARCH PRODUCT

Symplectic automorphisms of prime order on K3 surfaces

Alessandra SartiAlice Garbagnati

subject

Discrete mathematicsPure mathematicsAutomorphismsAlgebra and Number TheoryOuter automorphism groupK3 surfacesAutomorphismCohomologyMathematics - Algebraic GeometryMathematics::Group TheoryInner automorphism14J28 14J10FOS: MathematicsInvariant (mathematics)Algebraic numberComplex numberAlgebraic Geometry (math.AG)ModuliSymplectic geometryMathematics

description

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.

yearjournalcountryeditionlanguage
2006-03-31
https://dx.doi.org/10.48550/arxiv.math/0603742