We report on an adaptive, parallel, finite difference, additive multigrid code for the solution of partial differential equations. The code is based on two concepts: We use Hilbert's space-filling curves for the key based addressing of vertices and geometric entities. This enumeration scheme leads to a cheap and efficient way of geometric, dynamic data partitioning and migration on a parallel computer. Furthermore, it is used for the hash storage of the vertices, which is the novel second concept. This way traditional tree data structures are avoided, which can be annoying especially in parallel implementations.