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Book Review

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Book Information:

Author: 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 [Enhancements On Off] (What's this?)

  • 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

Review Information:

Reviewer: Christian Okonek
Journal: Bull. Amer. Math. Soc. 19 (1988), 528-530
American Mathematical Society