On the Geometry of Super Riemann Surfaces

  • Stephen KwokEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2027)


Super Riemann surfaces-1|1 complex supermanifolds with a SUSY-1 structure- 4 furnish a rich field of study in algebraic supergeometry.


Line Bundle Projective Space Ample Line Bundle Invertible Sheaf Invertible Sheave 
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  1. 1.
    D.G. Babbit, V.S. Varadarajan, Local moduli for meromorphic differential equations. Astérisque 169–170, 1–217 (1989)Google Scholar
  2. 2.
    A.M. Baranov, Y.I. Manin, I.V. Frolov, A.S. Schwarz, A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings. Comm. Math. Phys. 111(3), 373–392 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    C. Carmeli, L. Caston, R. Fioresi, Mathematical foundations of supersymmetry (In preparation)Google Scholar
  4. 4.
    C. Carmeli, R. Fioresi, Remarks on super distributions and super Harish-Chandra pairs (In preparation)Google Scholar
  5. 5.
    L. Crane, J., Rabin, Super Riemann surfaces: Uniformization and Teichmller theory. Comm. Math. Phys. 113(4), 601–623 (1988)Google Scholar
  6. 6.
    P. Deligne, Letters to Y.I. Manin (1987)Google Scholar
  7. 7.
    P. Deligne, Personal communication (2010)Google Scholar
  8. 8.
    P. Deligne, J. Morgan, Quantum Fields and Strings: A Course for Mathematicians, vol. 1 (AMS, RI, 1999)zbMATHGoogle Scholar
  9. 9.
    J.A. Dominguez Perez, D. Hernandez Ruiperez, C. Sancho de Salas, Global structures for the moduli of (punctured) super Riemann surfaces. J. Geom. Phys. 21(3), 199–217 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    P. Freund, J. Rabin, Supertori are elliptic curves. Comm. Math. Phys. 114(1), 131–145 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    C. Grosche, Selberg supertrace formula for super Riemann surfaces, analytic properties of zeta-functions and multiloop contributions for the fermionic string. Comm. Math. Phys. 133(3), 433–485 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    C. Grosche, Selberg super-trace formula for super Riemann surfaces. II. Elliptic and parabolic conjugacy classes, and Selberg super-zeta functions. Comm. Math. Phys. 151(1), 1–37 (1993)Google Scholar
  13. 13.
    C. Grosche, Selberg supertrace formula for super Riemann surfaces. III. Bordered super Riemann surfaces. Comm. Math. Phys. 162(3), 591–631 (1994)MathSciNetzbMATHGoogle Scholar
  14. 14.
    S. Kwok, Ph. D. thesis (in preparation)Google Scholar
  15. 15.
    A.M. Levin, Supersymmetric elliptic and modular functions. Funct. Anal. Appl. 22(1), 60–61 (1988)zbMATHCrossRefGoogle Scholar
  16. 16.
    Y.I. Manin, Gauge Field Theory and Complex Geometry (Springer, New York, 1988)zbMATHGoogle Scholar
  17. 17.
    Y.I. Manin, Topics in Noncommutative Geometry (Princeton University Press, Princeton, 1991)zbMATHGoogle Scholar
  18. 18.
    J. Rabin, Super elliptic curves. J. Geom. Phys. 15(3), 252–280 (1995)MathSciNetzbMATHGoogle Scholar
  19. 19.
    J. Rabin, M. Rothstein, D-modules on 1 | 1 supercurves. J. Geom. Phys. 60(4), 626–636 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    A.A. Rosly, A.S. Schwarz, A.A. Voronov, Geometry of superconformal manifolds. Comm. Math. Phys 1, 129–152 (1988)MathSciNetCrossRefGoogle Scholar
  21. 21.
    H. Salmasian, Unitary representations of nilpotent super Lie groups. arXiv: math.RT, 0906.2515Google Scholar
  22. 22.
    A.A. Voronov, Y.I., Manin, I.B. Penkov, Elements of supergeometry. J. Soviet Math. 51(1), 2069–2083 (1990)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at Los 52 AngelesLos AngelesUSA

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