CONFORMAL LIE-SUPERALGEBRAS AND MODULI SPACES

A conformal Lie superalgebra is a superextension of the centerless Virasoro algebra W-the Lie algebra of complex vector fields on the circle. The algebras of Ramond and Neveu-Schwarz are not the only examples of such superalgebras. All known superconformal algebras can be obtained as comlexifications of Lie superalgebras of vector fields on a supercircle with an additional structure. For every such superalgebra G a class of geometric objects-complex G-supercurves- is defined. For the superalgebras of Neveu-Schwarz and Ramond they are super Riemann surfaces with punctures of different kinds. We construct moduli superspaces for compact G-supercurves, and show that the superalgebra G acts infinitesimally on the corresponding moduli space.