Explicit formulae for cocycles of holomorphic vector fields with values in $\lambda$ densities

Abstract: In this article, 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, $\Sigma_r$ being a compact Riemann surface punctured in $r$ points This is done using the cocycles which have been evidenced by V. Ovsienko and C. Roger in [13] and globalizing them by their transformation property.

Classification (MSC2000): 17B56, 17B65, 17B66, 17B68

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