GRADED RIEMANN SURFACES AND KRICHEVER-NOVIKOV ALGEBRAS

Following the work of Krichever and Novikov, Bonora, Martellini, Rinaldi and Russo defined a superalgebra associated to each compact Riemann surface with spin structure. Noting that this data determines a graded Riemann surface, we find a natural interpretation of the BMRR-algebra in terms of the geometry of graded Riemann surfaces. We also discuss the central extensions of these algebras (correcting the form of the central extension given by Bonora et al.). It is hoped that this work will be the first step towards defining Krichever-Novikov algebras for (the more general) super-Riemann surfaces; in particular we emphasise the importance of graded conformal vectorfields. © 1990 Kluwer Academic Publishers.