Even and odd symplectic and K\"ahlerian structures on projective   superspaces
  Supergeneralization of $\DC P(N)$ provided by even and odd K\"ahlerian structures from Hamiltonian reduction are construct.Operator $ \Delta$ which used in Batalin-- Vilkovisky quantization formalism and mechanics which are bi-Hamiltonian under corresponding even and odd Poisson brackets are considered. 
O. N. Khudaverdian, A. P. Nersessian