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Ample vector bundles on a rational surface (higher rank)

Published online by Cambridge University Press:  22 January 2016

Toshio Hosoh
Toshio Hosoh*
Affiliation:
Nagoya University
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In the previous paper [1], we showed that the set of simple vector bundles of rank 2 on a rational surface with fixed Chern classes is bounded and we gave a sufficient condition for an H-stable vector bundle of rank 2 on a rational surface to be ample. In this paper, we shall extend the results of [1] to the case of higher rank.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 66 , May 1977 , pp. 77 - 88
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1977

References

[1] Hosoh, T., Ample vector bundles on a rational surface, Nagoya Math. J., 59 (1975), 135–148.Google Scholar
[2] Kleiman, S., Les théorèmes de finitude pour foncteur de Picard, SGA 6, exposé 13.Google Scholar
[3] Maruyama, M., On a family of algebraic vector bundles, Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, Kinokuniya, Tokyo (1973), 95–146.Google Scholar
[4] Schwarzenberger, R. E. L., Vector bundles on algebraic surfaces, Proc. London Math. Soc, (3), 11 (1961), 601–622.Google Scholar
[5] Takemoto, F., Stable vector bundles on algebraic surfaces, Nagoya Math. J., 47 (1972), 29–48.CrossRefGoogle Scholar