  Pure spinor formalism implies that supergravity equations in space-time are
equivalent to the requirement that the worldsheet sigma-model satisfies certain
properties. Here we point out that one of these properties has a particularly
transparent geometrical interpretation. Namely, there exists an odd nilpotent
vector field on some singular supermanifold, naturally associated to
space-time. All supergravity fields are encoded in this vector field, as
coefficients in its normal form. The nilpotence implies, modulo some zero
modes, that they satisfy the SUGRA equations of motion.
