ABSTRACT
In this respect, a good example where the picture is completely clear is the classification of complex analytic structures on a fixed topological manifold. Also in algebraic geometry one has well-developed results in this direction. Recall for instance that for the moduli space M.g of smooth projective curves of genus g over C (or equivalentiy, compact Riemann surfaces of genus g) the tangent space T\C}Mg can be naturally identified with H1(CI, TC), where TC is the sheaf of holornorphic 1991 Mathematics Subject Classification. Primary: 17B66; Secondary: 17B56, 17B65, 17B68, 14D15, 14H52. Key words and phrases. Deformations of algebras, rigidity, Witt algebra, Virasoro algebra, Krichever-Novikov algebras, elliptic curves, Lie algebra cohomology. This research was partially supported by the grants OTKA T030823, T29525.
