Abstract
We generalize the Kodaira Embedding Theorem and Chow's Theorem to the context of families of complex supermanifolds. In particular, we show that every family of super Riemann surfaces is a family of projective superalgebraic varieties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batchelor, M.: The structure of supermanifolds. Trans. Am. Math. Soc.253, 329–338 (1979)
Berezin, F. A.: Method of second quantization. Pure and Applied Physics, vol. 24. NY: Academic Press 1966
Chow, W. L.: On Compact Complex Analytic Varieties. Am. J. Math.71, 893–914 (1949)
Deligne, P.: Letter to Y.I. Manin
Eastwood, M., LeBrun, C.: Thickening and Supersymmetric Extensions of Complex Manifolds. Am. J. Math.108, 1177–1192 (1986)
Friedan, D.: Notes on string theory and two-dimensional conformal Field Theory. EFI preprint 85-99 (1985)
Grauert, H.: Ein Theorem der analytischen Garben theorie and die Modulräume komplexer Strukturen. Publ. Inst. Hautes Études Scientifiques5, 233–292 (1960)
Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann.146, 331–368 (1962).
Green, M. B., Schwarz, J. H., Witten, E.: Superstring Theory I & II. Cambridge Monographs on Mathematical Physics. Cambridge, MA: Cambridge University Press 1987
Griffiths, P.: The extension problem in complex analysis II, embeddings with positive normal bundle. Am. J. Math.88, 366–466 (1966)
Gunning, R.: Lectures on Riemann Surface. Princeton, NJ: Princeton University Press 1966
Michio Kaku: Introduction to SuperStrings. Berlin, Heidelberg, New York: Springer 1988
Kodaira, K.: On Kähler Varieties of Restricted Type (an Intrinsic Characterization of Algebraic Varieties). Ann. Math.60, 28–48 (1954)
Kodaira, K., Spencer, D. C.: On deformation of complex analytic structure, III. Ann. Math.71, 43–76 (1960)
LeBrun, C., Rothstein, M.: Moduli of super Riemann surfaces. Commun. Math. Phys.117, 159–176 (1988)
Neveu, A., Schwartz, J. H.: Factorizable Dual Model of Pions. Nucl. Phys.B31, 86–112 (1971)
Manin, Y. I.: Gauge field theory and complex geometry. Berlin, Heidelberg, New York: Springer 1988
Mumford, D.: Stability of projective varieties. L'Ens. Math.23, 39–110 (1977)
Penkov, I. B., Skornyakov, I. A.: Projectivity andD-affinity of Flag Supermanifolds. Russ. Math. Surv.40, 233–234 (1987)
Ramond, P.: Dual theory of free fermions. Phys. Rev.D3, 2415–2418 (1971)
Rabin, J., Topiwala, P.: Super-Space GAGA and Moduli of SRS's. University of Chicago, preprint (1988)
Rothstein, M.: Deformation of complex supermanifolds. Proc. Am. Math. Soc.95, 255–260 (1985)
Rothstein, M.: Integration on Non-compact Supermanifolds. Trans. Am. Math. Soc.299, 387 (1987)
Wells, Jr, R. O.: Differential analysis on complex manifolds. Berlin, Heidelberg, New York: Springer 1982
Whitney, H.: The Self-intersections of a Smoothn-Manifold in 2n-Space. Ann. Math.45, 247–293 (1944)
Wess, J., Zumino, B.: Supergauge transformations in four dimensions. Nucl. Phys.B70, 39–50 (1974)
Author information
Authors and Affiliations
Additional information
Communicated by L. Alvarez-Gaumé
Research supported in part by NSF grant DMS-8704401
Research supported in part by NSF grant DMS-4253943
Research also supported in part by NSF grant DMS-4253943
Rights and permissions
About this article
Cite this article
LeBrun, C., Poon, YS. & Wells, R.O. Projective embeddings of complex supermanifolds. Commun.Math. Phys. 126, 433–452 (1990). https://doi.org/10.1007/BF02125694
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02125694