  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. Is it true that all supergravity fields are encoded in this vector
field, as coefficients in its normal form, and the nilpotence is equivalent to
the target space equations of motion? We show that this is approximately
correct. The normal form is parametrized by some tensor fields, which satisfy
hyperbolic equations. These equations are slightly weaker than the full
supergravity equations.
