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.
@article{hal-00008866,
author = {Wagemann, Friedrich},
title = {Explicit Formulae for Cocycles of Holomorphic Vector Fields with values in lambda-Densities},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00008866}
}
Wagemann, Friedrich. Explicit Formulae for Cocycles of Holomorphic Vector Fields with values in lambda-Densities. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-00008866/