Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-04T21:05:43.910Z Has data issue: false hasContentIssue false
  • English
  • Français

Moduli spaces of compact complex submanifolds of complex fibered manifolds

Published online by Cambridge University Press:  24 October 2008

Sergey A. Merkulov
Sergey A. Merkulov
Affiliation:
School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA
Get access Rights & Permissions [Opens in a new window]

Extract

In 1962 Kodaira[11] proved that ifX ↪ Y is a compact complex submanifold with normal bundle N such that H1(X, N) = 0, then X belongs to a locally complete family {Xt: t ∈ M} of complex submanifolds Xt of Y with the moduli space M being a (dimcH0(X, N))-dimensional complex manifold, and there exists a canonical isomorphism

between the tangent space of M at a point t ∈ M and the space of all global sections of the normal bundle Nt of the embedding Xt ↪ Y.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 71 - 91
Copyright
Copyright © Cambridge Philosophical Society 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ambrose, W. and Singer, I. M.. A theorem on holonomy. Trans. Amer. Math. Soc. 79 (1953), 428–443.CrossRefGoogle Scholar
[2]Bailey, T. N. and Eastwood, M. G.. Complex paraconformal manifolds – their differential geometry and twistor theory. Forum Math. 3 (1991), 61–103.CrossRefGoogle Scholar
[3]Boyer, C. P.. A note on hyperhermitian four-manifolds. Proc. Amer. Math. Soc. 102 (1988), 157–164.Google Scholar
[4]Bryant, R.. Two exotic holonomies in dimension four, path geometries, and twistor theory. Proc. Symposia in Pure Mathematics 83 (1991), 33–88.CrossRefGoogle Scholar
[5]Curtis, W. D., Lerner, D. E. and Miller, F. R.. Complex pp waves and the nonlinear graviten construction. J. Math. Phys. 19 (1978), 2024–2027.CrossRefGoogle Scholar
[6]Eastwood, M. G. and LeBrun, C. R.. Fattening complex manifolds: curvature and Kodaira-Spencer maps. J. Geom. Phys. 8 (1992), 123–146.CrossRefGoogle Scholar
[7]Grauert, H. and Remmert, R.. Coherent analytic sheaves (Springer, 1984).CrossRefGoogle Scholar
[8]Griffiths, P. A.. The extension problem in complex analysis II: embeddings with positive normal bundle. Amer. J. Math. 88 (1966), 366–446.CrossRefGoogle Scholar
[9]Hitchin, N. J., Karlhede, A., LindströM, U. and Roček, M.. HyperKähler metrics and supersymmetry. Commun. Math. Phys. 108 (1987), 535–589.CrossRefGoogle Scholar
[10]Kobayashi, S. and Nomizu, K.. Foundations of differential geometry, vol. II (Wiley, 1969).Google Scholar
[11]Kodaira, K.. A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds. Ann. Math. 75 (1962), 146–162.CrossRefGoogle Scholar
[12]Kodaira, K.. Complex manifolds and deformations of complex structures (Springer, 1986).CrossRefGoogle Scholar
[13]Pedersen, H. and Swann, A.. Riemannian submersions, four-manifolds and Einstein-Weyl geometry. Proc. London Math. Soc. 66 (1993), 381–399.CrossRefGoogle Scholar
[14]Penrose, R.. Nonlinear gravitons and curved twistor theory. Gen. Bel. Grav. 7 (1976), 31–52.CrossRefGoogle Scholar
[15]Salamon, S. M.. Differential geometry of quaternionic manifolds. Ann. Scient. EC. Norm. Sup. 4e série, 19 (1986), 31–55.CrossRefGoogle Scholar
[16]Tod, K. P. and Ward, R. S.. Self-dual metrics with self-dual Killing vectors. Proc. R. Soc. Lond. A 368 (1979), 411–427.Google Scholar
[17]Ward, R. S.. A class of self-dual solutions of Einstein's equations. Proc. R. Soc. Lond. A 363 (1978), 289–295.Google Scholar