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Moduli of super Riemann surfaces

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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.

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References

  1. 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

    Google Scholar 

  2. Atiyah, M.: Riemann surfaces and spin structures. Ann. Sci. Ec. Norm. Super., Ser. 4, t.4, 47–62 (1971)

    Google Scholar 

  3. Bers, L., Ehrenpreis, L.: Holomorphic convexity of Teichmüller spaces. Bull. AMS70, 761–764 (1964)

    Google Scholar 

  4. Crane, L., Rabin, J.M.: Super Riemann surfaces: uniformization and Teichmüller theory. Commun. Math. Phys.113, 601–623 (1988)

    Google Scholar 

  5. Earle, C.J., Kra, I.: Half-canonical divisors on variable Riemann surfaces. J. Math. Kyoto Univ.26, 39–64 (1986)

    Google Scholar 

  6. Eastwood, M., Le Brun, C.: Thickenings and supersymmetric extensions of complex manifolds. Am. J. Math.108, 1177–1192 (1986)

    Google Scholar 

  7. Farkas, H., Kra, I.: Riemann surfaces. Graduate texts in mathematics, Vol. 71. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

  8. Freidan, D.: Notes on string theory and two dimensional conformal field theory. EFI preprint 85–99

  9. Grothendieck, A.: Construction de l'espace de Teichmüller. Sem. Henri Cartan13 (1961) exposé 17

    Google Scholar 

  10. Johnson, D.: Spin structures and quadratic forms on surfaces. J. Lond. Math. Soc. (2),22, 365–373 (1980)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. Rothstein, M.: Deformations of complex supermanifolds. Proc. AMS95, 255–260 (1985)

    Google Scholar 

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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)

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LeBrun, C., Rothstein, M. Moduli of super Riemann surfaces. Commun.Math. Phys. 117, 159–176 (1988). https://doi.org/10.1007/BF01228415

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  • DOI: https://doi.org/10.1007/BF01228415

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