Complex reflection groups and K3 surfaces I

We construct here many families of K3 surfaces that one can obtain as quotients algebraic by some subgroups the rank four complex reflection groups. find in total 15 with at worst $ADE$--singularities. In particular we classify all be obtained derived subgroup previous prove our results using geometry weighted projective spaces where these are embedded and theory Springer Lehrer-Springer on properties This construction generalizes a W. Barth second author.