Abstract
We recall some deformation theory of susy-curves and construct the local model of their (compactified) moduli ‘spaces’. We also construct universal deformations “concentrated” at isolated points, which are the mathematical counterparts of the usual choices done in the physical literature. We argue that these cannot give a projected “atlas” for supermoduli spaces.
Keywords
- Modulus Space
- Line Bundle
- Spin Curve
- Weierstrass Point
- Versal Deformation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Work partially supported by the national project “Geometria e Fisica” M.P.I.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
E. Arbarello, M. Cornalba, P. Griffiths, J. Harris, Geometry of algebraic curves Vol I, Grund. Math. Wiss. 267, Springer Verlag (Berlin), (1986).
M. Bershadsky, Super-Riemann surfaces, loop measure etc. … Nucl. Phys. B 310, 79, (1988).
M. Cornalba, Moduli of curves and theta-characteristics. Preprint, Universita' di Pavia, (1988).
P. Deligne, unpublished letter to Yu.I. Manin, (1987).
P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Publ. Math. I.H.E.S. 36, 75 (1969).
E. D'Hoker, D.H. Phong, The geometry of string perturbation theory. Preprint, to appear in Rev. Mod. Phys. 60 (1988).
D. Friedan, Notes on string theory and two dimensional conformal field theory. In Unified String Theories, M. Green, D. Gross eds. (1986) World Scientific (Singapore).
D. Friedan, E. Martinec, S. Shenker, Conformal invariance, supergravity and string theory. Nucl. Phys. B 271 (1986) 93.
G. Falqui and C. Reina, (in preparation).
S.B. Giddings, P. Nelson, The geometry of super Riemann surfaces Commun. Math. Phys. 116, 607, (1988).
R. Hartshorne, Algebraic Geometry, GTM 52 Springer Verlag (Berlin), (1977).
P.S. Howe, Super Weyl transformations in two dimensions. J. Phys. A: Math. Gen., 12, 393 (1979).
D.A. Leites, Introduction to the theory of supermanifolds. Russ. Math. Surveys 35, 1 (1980).
C. LeBrun, M. Rothstein, Moduli of Super Riemann Surfaces. Commun. Math. Phys. 117, 159 (1988).
M. Martellini, P. Teofilatto, Global structure of the superstring partition function and resolution of the supermoduli measure ambiguity. Phys. Lett. 211B, 293 (1988).
Yu.I. Manin, Critical dimensions of the string theories and the dualizing sheaf on the moduli space of (super) curves. Funct. Anal. Appl. 20, 244 (1987).
M. Rothstein, Deformations of complex supermanifolds. Proc. Amer. Math. Soc. 95, 255 (1985).
M. Rothstein, Integration on noncompact supermanifolds. Trans. Amer. Math. Soc. 299, 387 (1987).
A.Yu. Waintrob, Deformations of complex structures on supermanifolds, Seminar on supermanifolds no 24 D. Leites ed., ISSN 0348-7662, University of Stockholm (1988).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Falqui, G., Reina, C. (1990). Supermoduli and superstrings. In: Francaviglia, M., Gherardelli, F. (eds) Global Geometry and Mathematical Physics. Lecture Notes in Mathematics, vol 1451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085070
Download citation
DOI: https://doi.org/10.1007/BFb0085070
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53286-6
Online ISBN: 978-3-540-46813-4
eBook Packages: Springer Book Archive
