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Projective structures on moduli spaces of compact complex hypersurfaces
Author(s):
Sergey
Merkulov;
Henrik
Pedersen
Journal:
Proc. Amer. Math. Soc.
125
(1997),
407-416.
MSC (1991):
Primary 32G10, 32L25, 53A15, 53B05, 53B10
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Abstract:
It is shown that moduli spaces of complete families of compact complex hypersurfaces in complex manifolds often come equipped canonically with projective structures satisfying some natural integrability conditions.
References:
- [A]
- M. F. Atiyah, The signature of fibre bundles, in Global Analysis, Papers in honor of K. Kodaira (D. C. Spencer and S. Yanaga, eds.), Princeton Univ. Press, Princeton, 1969, 73-84. MR 40:8071
- [H]
- N. Hitchin, Complex manifolds and Einstein's equations, In: H. D. Doebner, et al. (eds.) Twistor geometry and non-linear systems, Lect. Notes Math., vol. 970, Springer-Verlag, Berlin, Heidelberg, New York, 1982, pp. 73-99. MR 84i:32041
- [K-1]
- K. Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math. 75 (1962), 146-162. MR 24:A3665b
- [K-2]
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- [K-3]
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- [L]
- C. LeBrun, Spaces of complex geodesics and related structures, D. Phil. Thesis, Oxford University, 1980.
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- H. Pedersen, Einstein-Weyl Spaces and
 -Curves in the Quadric Surface, Ann. Global Anal. Geom. 4 (1986), 89-120. MR 88j:53045 - [PT]
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- [Pe]
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Additional Information:
Sergey
Merkulov
Affiliation:
School of Mathematics and Statistics, University of Plymouth, Plymouth, Devon PL4 8AA, United Kingdom
Address at time of publication:
Department of Pure Mathematics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, United Kingdom
Henrik
Pedersen
Affiliation:
Department of Mathematics and Computer Science, Odense University, Campusvej 55, 5230 Odense M, Denmark
DOI:
10.1090/S0002-9939-97-03408-4
PII:
S 0002-9939(97)03408-4
Received by editor(s):
April 12, 1994
Received by editor(s) in revised form:
April 13, 1995
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1997,
American Mathematical Society
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