PROJECTIVE UNIFORMIZATION AND GRADED LIE-ALGEBRAS ON RIEMANN SURFACES

I show that any Reimann surfaces S is endowed with a natural sheaf of graded Lie algebras A which is related to the projective uniformization of S. Moreover the cohomology set H-1(S,A), which turns out to be direct sum of two Eichler cohomology groups, contains all the ingredient to define a super Reimann structure on S and to investigate its space of moduli.