Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-23T11:00:19.851Z Has data issue: false hasContentIssue false
  • English
  • Français

Stable vector bundles on algebraic surfaces II

Published online by Cambridge University Press:  22 January 2016

Fumio Takemoto
Fumio Takemoto*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is a continuation of “Stable vector bundles on algebraic surfaces” [10]. For simplicity we deal with non-singular projective varieties over the field of complex numbers. Let W be a variety whose fundamental group is solvable, let H be an ample line bundle on W, and let f: V → W be an unramified covering. Then we show in section 1 that if E is an f*H-stable vector bundle on V then f*E is a direct sum of H-stable vector bundles. In particular f*L is a direct sum of simple vector bundles if L is a line bundle on V.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 52 , December 1973 , pp. 173 - 195
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Atiyah, M. F., Vector bundles over an elliptic curve, Proc. London Math. Soc, (3) 7 (1957), 414–452.CrossRefGoogle Scholar
[2] Grothendieck, A., Sur une note de Mattuck-Tate, J. reine angew. Math., 20 (1958), 208–215.Google Scholar
[3] Kodaira, K., On compact analytic surfaces II, Annals of Math., 77 (1963), 563–626.CrossRefGoogle Scholar
[4] Morikawa, H., A note on holomorphic vector bundles over complex tori, Nagoya Math. J., 41 (1971), 101–106.Google Scholar
[5] Mumford, D., Abelian varieties, Oxford Univ. Press, 1970.Google Scholar
[6] Oda, T., Vector bundles on an elliptic curve, Nagoya Math. J., 43 (1971), 41–72.Google Scholar
[7] Oda, T., Vector bundles on abelian surfaces, Invent. Math., 13 (1971), 249–260.CrossRefGoogle Scholar
[8] Safarevic, I. R. and others, Algebraic surfaces, Moskva 1965.Google Scholar
[9] Suwa, T., On hyperelliptic surfaces, J. of the Faculty of Sci. Univ. of Tokyo, 16 (1969–1970), 469–476.Google Scholar
[10] Takemoto, F., Stable vector bundles on algebraic surfaces, Nagoya Math. J., 47 (1972), 29–48.Google Scholar
[11] Van de Ven, A., On the Chern numbers of certain complex and almost complex manifolds, Proc. Nat. Acad. Sci., U.S.A., 55 (1966), 1624-1627.Google Scholar