Explicit Formulae for Cocycles of Holomorphic Vector Fields with values   in lambda-Densities
  We give explicit formulae for the generators of H^2(Hol(\Sigma_r,{\cal F}_{\lambda}(\Sigma_r)) in terms of affine and projective connections. This is done using the cocycles of V. Ovsienko and C. Roger for the case of the circle and globalizing them to an open Riemann surface \Sigma_r. 
Friedrich Wagemann