Abstract
We recall some deformation theory of Susy-curves and study obstructions to projectedness of supermoduli spaces, both from a general standpoint and by means of the local “coordinate charts” most commonly used in the physical literature. We prove that these give rise to a projected atlas for genusg=2 only.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[AG] Alvarez-Gaumé, L.: private communication
[AMS] Atick, J., Moore, G., Sen, A.: Some global issues in string perturbation theory. Nucl. Phys.B308, 1 (1988)
[B] Bershadsky, M.: Super-Riemann surfaces, loop measure, etc. ... Nucl. Phys.B310, 79 (1988)
[BMFS] Baranov, A. M., Manin, Yu. I., Frolov, I. V., Schwarz, A. S.: A superanalog of the Selberg trace formula and multiloop contributions for fermionic strings. Commun. Math. Phys.111, 373 (1987) and the references quoted therein
[C] Cornalba, M.: Moduli of curves and theta-characteristics. Preprint, Universita' di Pavia, (1988)
[CR] Crane, I., Rabin, J. M.: Super Riemann Surfaces: Uniformization and Teichmüller Theory. Commun. Math. Phys.113, 601 (1988)
[D] Deligne, P.: unpublished letter to Manin, Yu. I., (1987)
[DM] Deligne, P., Mumford, D.: The irreducibility of the space of curves of a given genus. Publ. Math. I.H.E.S.36, 75 (1969)
[DP] D'Hoker, E., Phong, D. H.: The geometry of string perturbation theory. Rev. Mod. Phys.60, 917 (1988)
[F] Friedan, D.: Notes on string theory and two dimensional conformal field theory. In: Unified string theories. Green, M., Gross, D. (eds.) Singapore: World Scientific 1986
[FR] Falqui, G., Reina, C.: Superstrings and Supermoduli, to be published in: Proceedings of the 1988 C.I.M.E. summer course “Global Geometry and Mathematical Physics,” Montecatini 1988
[FMRT] Falqui, G., Martellini, M., Reina, C., Teofilatto, P.: Some remarks on an algebrogeometrical approach to Superstring theory. Proceedings of the 8th Italian Conference on General Relativity and Gravitational Physics, Cerdonio, M. et al., eds., 368, Singapore: World Scientific 1989
[GIS] Gava, E., Iengo, R., Sotkov, G.: Modular invariance and the two-loop vanishing of the cosmological constant. Phys. Lett.207B, 283 (1988)
[K] Kodaira, K.: Complex manifolds and deformation of complex structures. Grundlehren der mathematischen Wissenschaften vol.283. Berlin, Heidelberg, New York: Springer 1986
[LN] La, H. S., Nelson, P.: Effective field equations for fermionic strings preprint BUHEP-89-9/UPR-0391T
[LR] LeBrun, C., Rothstein, M.: Moduli of super Riemann surfaces. Commun. Math. Phys.117, 159 (1988)
[M] 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 (1987)
[MT] Martellini, M., Teofilatto, P.: Global structure of the superstring partition function and resolution of the supermoduli measure ambiguity. Phys. Lett.211B, 293 (1988)
[Mu] Mumford, D.: Picard groups of moduli problems. In: Arithmetical algebraic geometry, Schilling, O. F. G. (ed.) New York: Harper & Row 33 1965
[P] Popp, H.: Moduli theory and classification theory of algebraic varieties. Lecture Notes in Mathematics vol.620 Berlin, Heidelberg, New York: Springer 1977
[R] Rothstein, M.: Integration on noncompact supermanifolds. Trans. Am. Math. Soc.299, 387 (1987)
[V] Voronov, A. A.: A formula for Mumford's measure in Superstring theory. Funct. Anal. Appl.22, 139 (1989)
[W] Waintrob, A. Yu.: Deformations of complex structures on supermanifolds. Seminar on supermanifolds no. 24 Leites, D. (ed.), ISSN 0348-7662, University of Stockholm (1988)
Author information
Authors and Affiliations
Additional information
Communicated by L. Alvarez-Gaumé
Work partially supported by the National Project “Geometria e Fisica”, M.P.I.
Rights and permissions
About this article
Cite this article
Falqui, G., Reina, C. A note on the global structure of supermoduli spaces. Commun.Math. Phys. 128, 247–261 (1990). https://doi.org/10.1007/BF02108781
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02108781