A projection to the pure spinor space

This article is based on a talk given at the Memorial Conference for Maximilian Kreuzer at the ESI in Vienna and contains a compact summary of a recent collaboration with P. A. Grassi. A nonlinear projection from the space of SO(10) Weyl spinors to the space of pure spinors is presented together with some of its particular properties. This projection can be used to remove the constraints from Berkovits' pure spinor superstring while introducing additional gauge symmetries. This should allow to make transitions to equivalent formulations which might shed light on the origin of the pure spinor ghosts. It might also be useful in the context of path integral measures for the pure spinor string.