Abstract
The basic properties of super Riemann surfaces are presented, and their supermoduli spaces are constructed, in a manner suitable for the application of algebro-geometric techniques to string theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahlfors, L.: The complex analytic structure of the space of closed Riemann surfaces. In Analytic functions, pp. 349–376. Princeton, NJ: Princeton University Press 1960
Atiyah, M.: Riemann surfaces and spin structures. Ann. Sci. Ec. Norm. Super., Ser. 4, t.4, 47–62 (1971)
Bers, L., Ehrenpreis, L.: Holomorphic convexity of Teichmüller spaces. Bull. AMS70, 761–764 (1964)
Crane, L., Rabin, J.M.: Super Riemann surfaces: uniformization and Teichmüller theory. Commun. Math. Phys.113, 601–623 (1988)
Earle, C.J., Kra, I.: Half-canonical divisors on variable Riemann surfaces. J. Math. Kyoto Univ.26, 39–64 (1986)
Eastwood, M., Le Brun, C.: Thickenings and supersymmetric extensions of complex manifolds. Am. J. Math.108, 1177–1192 (1986)
Farkas, H., Kra, I.: Riemann surfaces. Graduate texts in mathematics, Vol. 71. Berlin, Heidelberg, New York: Springer 1980
Freidan, D.: Notes on string theory and two dimensional conformal field theory. EFI preprint 85–99
Grothendieck, A.: Construction de l'espace de Teichmüller. Sem. Henri Cartan13 (1961) exposé 17
Johnson, D.: Spin structures and quadratic forms on surfaces. J. Lond. Math. Soc. (2),22, 365–373 (1980)
Kodaira, K., Spencer, D.C.: On deformations of complex analytic structures. I, II. Ann. Math.67, 328–466 (1958); II. Ann. Math.71, 43–76 (1960)
Manin, Yu.I.: Critical dimensions of the string theories and the dualizing sheaf on the moduli space of (super) curves. Funct. Anal. Appl.20, 244–245 (1987)
Rothstein, M.: Deformations of complex supermanifolds. Proc. AMS95, 255–260 (1985)
Author information
Authors and Affiliations
Additional information
Communicated by L. Alvarez-Gaumé
Supported in part by NSF Grant No. DMS-8704401
Supported in part by NSF Grants No. DMS-8501783 and No. DMS-86107301(1)
Rights and permissions
About this article
Cite this article
LeBrun, C., Rothstein, M. Moduli of super Riemann surfaces. Commun.Math. Phys. 117, 159–176 (1988). https://doi.org/10.1007/BF01228415
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01228415