Geometry of Kodaira moduli spaces

Merkulov, Sergey

doi:10.1090/S0002-9939-96-03354-0

Geometry of Kodaira moduli spaces
HTML articles powered by AMS MathViewer

by Sergey A. Merkulov PDF

Proc. Amer. Math. Soc. 124 (1996), 1499-1506 Request permission

Abstract:

A general theorem on the existence of natural torsion-free affine connections on a complete family of compact complex submanifolds in a complex manifold is proved.

References

T. N. Bailey and R. J. Baston (eds.), Twistors in mathematics and physics, London Mathematical Society Lecture Note Series, vol. 156, Cambridge University Press, Cambridge, 1990. MR 1089905, DOI 10.1017/CBO9781107325821
Toby N. Bailey and Michael G. Eastwood, Complex paraconformal manifolds—their differential geometry and twistor theory, Forum Math. 3 (1991), no. 1, 61–103. MR 1085595, DOI 10.1515/form.1991.3.61
Robert J. Baston and Michael G. Eastwood, The Penrose transform, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Its interaction with representation theory; Oxford Science Publications. MR 1038279
Arthur L. Besse, Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, Springer-Verlag, Berlin, 1987. MR 867684, DOI 10.1007/978-3-540-74311-8
Charles P. Boyer, A note on hyper-Hermitian four-manifolds, Proc. Amer. Math. Soc. 102 (1988), no. 1, 157–164. MR 915736, DOI 10.1090/S0002-9939-1988-0915736-8
Michael Eastwood and Claude LeBrun, Fattening complex manifolds: curvature and Kodaira-Spencer maps, J. Geom. Phys. 8 (1992), no. 1-4, 123–146. MR 1165875, DOI 10.1016/0393-0440(92)90045-3
Stephen Huggett (ed.), Twistor theory, Lecture Notes in Pure and Applied Mathematics, vol. 169, Marcel Dekker, Inc., New York, 1995. MR 1306951
N. J. Hitchin, Complex manifolds and Einstein’s equations, Twistor geometry and nonlinear systems (Primorsko, 1980) Lecture Notes in Math., vol. 970, Springer, Berlin-New York, 1982, pp. 73–99. MR 699802
A. Gloden, Sur la résolution en nombres entiers du système $A^{kx}+B^{kx}+C^{kx}+D^{kx}=E^x+F^x+G^x+H^x$ ($x=1$, $2$ et $3$), Bol. Mat. 12 (1939), 118–122 (French). MR 24
Claude LeBrun, Quaternionic-Kähler manifolds and conformal geometry, Math. Ann. 284 (1989), no. 3, 353–376. MR 1001707, DOI 10.1007/BF01442490
Yu. I. Manin, Gauge Field theory and Complex Geometry, Nauka, Moscow 1984.
S. A. Merkulov, Moduli of compact submanifolds of complex fibred manifolds, to appear in Math. Proc. Cambridge Phil. Soc.
—, Geometry of relative deformations I, In Twistor theory, Marcel Dekker, 1994, to appear.
S. A. Merkulov and H. Pedersen, Geometry of relative deformations II, In Twistor theory, Marcel Dekker 1994, to appear.
Henrik Pedersen and Y. Sun Poon, Twistorial construction of quaternionic manifolds, Proceedings of the Sixth International Colloquium on Differential Geometry (Santiago de Compostela, 1988) Cursos Congr. Univ. Santiago de Compostela, vol. 61, Univ. Santiago de Compostela, Santiago de Compostela, 1989, pp. 207–218. MR 1040847
Henrik Pedersen and Andrew Swann, Riemannian submersions, four-manifolds and Einstein-Weyl geometry, Proc. London Math. Soc. (3) 66 (1993), no. 2, 381–399. MR 1199072, DOI 10.1112/plms/s3-66.2.381
Roger Penrose, Nonlinear gravitons and curved twistor theory, Gen. Relativity Gravitation 7 (1976), no. 1, 31–52. MR 439004, DOI 10.1007/bf00762011
Roger Penrose and Wolfgang Rindler, Spinors and space-time. Vol. 2, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1986. Spinor and twistor methods in space-time geometry. MR 838301, DOI 10.1017/CBO9780511524486
R. S. Ward, On self-dual gauge fields, Phys. Lett. A 61 (1977), no. 2, 81–82. MR 443823, DOI 10.1016/0375-9601(77)90842-8
R. S. Ward, Self-dual space-times with cosmological constant, Comm. Math. Phys. 78 (1980/81), no. 1, 1–17. MR 597028, DOI 10.1007/BF01941967
R. S. Ward and Raymond O. Wells Jr., Twistor geometry and field theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1990. MR 1054377, DOI 10.1017/CBO9780511524493