Bulletin of the American Mathematical Society

MathSciNet review: 1567716
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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.

M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523–615. MR 702806, DOI 10.1098/rsta.1983.0017

S. K. Donaldson, Anti self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc. (3) 50 (1985), no. 1, 1–26. MR 765366, DOI 10.1112/plms/s3-50.1.1

S. K. Donaldson, Infinite determinants, stable bundles and curvature, Duke Math. J. 54 (1987), no. 1, 231–247. MR 885784, DOI 10.1215/S0012-7094-87-05414-7

S. K. Donaldson, Irrationality and the $h$-cobordism conjecture, J. Differential Geom. 26 (1987), no. 1, 141–168. MR 892034

Robert Friedman and John W. Morgan, On the diffeomorphism types of certain algebraic surfaces. I, J. Differential Geom. 27 (1988), no. 2, 297–369. MR 925124

Martin Lübke, Stability of Einstein-Hermitian vector bundles, Manuscripta Math. 42 (1983), no. 2-3, 245–257. MR 701206, DOI 10.1007/BF01169586

M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567. MR 184252, DOI 10.2307/1970710

Christian Okonek, Michael Schneider, and Heinz Spindler, Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser, Boston, Mass., 1980. MR 561910

C. Okonek and A. Van de Ven, Stable bundles and differentiable structures on certain elliptic surfaces, Invent. Math. 86 (1986), no. 2, 357–370. MR 856849, DOI 10.1007/BF01389075

K. Uhlenbeck and S.-T. Yau, On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S257–S293. Frontiers of the mathematical sciences: 1985 (New York, 1985). MR 861491, DOI 10.1002/cpa.3160390714

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 0702806

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