  The $b$-ghost of the pure spinor formalism in a general curved background is
not holomorphic. For such theories, the construction of the string measure
requires the knowledge of the action of diffeomorphisms on the BV phase space.
We construct such an action for the pure spinor sigma-model in $AdS_5\times
S^5$. From the point of view of the BV formalism, this sigma-model belongs to
the class of theories where the expansion of the Master Action in antifields
terminates at the quadratic order. We show that it can be reduced to a simpler
degenerate sigma-model, preserving the AdS symmetries. We construct the action
of the algebra of worldsheet vector fields on the BV phase space of this
minimalistic sigma-model, and explain how to lift it to the original model.
