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Book Review
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Book Information
Author(s):
Shoshichi Kobayashi
Title:
Differential geometry of complex vector bundles
Additional book information:
Publications of the Mathematical Society of Japan, no. 15 Iwanami Shoten Publishers and Princeton University Press, Princeton, N. J., 1987, xi+304 pp., $57.50. ISBN 0-691-08467-x
References:
- 1.
- M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1982), 523-615. MR 702806
- 2.
- S. K. Donaldson, Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. 50 (1985), 1-26. MR 765366
- 3.
- S. K. Donaldson, Infinite determinants-stable bundles and curvature, Duke Math. J. 54 (1987), 231-247. MR 885784
- 4.
- S. K. Donaldson, Irrationality and the h-cobordism conjecture, J. Differential Geom. 26 (1987), 141-168. MR 892034
- 5.
- R. Friedmann and J. W. Morgan, On the diffeomorphism types of certain algebraic surfaces. I, II, J. Differential Geom. (to appear). MR 925124
- 6.
- M. Lübke, Stability of Einstein-Hermitian vector bundles, Manuscripta Math. 42 (1983), 245-257. MR 701206
- 7.
- M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on compact Riemann surfaces, Ann. of Math. (2) 82 (1965), 540-567. MR 184252
- 8.
- C. Okonek, M. Schneider and H. Spindler, Vector bundles over complex projective space, Progress in Math., vol. 3, Birkhäuser, Boston, Basel, Stuttgart, 1980. MR 561910
- 9.
- C. Okonek and A. Van de Ven, Stable vector bundles and differentiable structures on certain elliptic surfaces, Invent. Math. 86 (1986), 357-370. MR 856849
- 10.
- K. K. Uhlenbeck and S.-T. Yau, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986), 257-293. MR 861491
Additional Information:
Reviewer(s):
Christian
Okonek
Review Information:
Journal:
Bull. Amer. Math. Soc.
19
(1988),
528-530.
DOI:
10.1090/S0273-0979-1988-15731-X
PII:
S 0273-0979(1988)15731-X
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