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A geometrical characterization of a class of holomorphic vector bundles over a complex torus

Published online by Cambridge University Press:  22 January 2016

Jun-Ichi Hano
Jun-Ichi Hano*
Affiliation:
Washington University
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This note is to be a supplement of the preceeding paper in the journal by Matsushima, settling a question raised by him. In his paper he associates a holomorphic vector bundle over a complex torus to a holomorphic representation of what he calls Heisenberg group. We shall show that a simple holomorphic vector bundle is determined in this manner if and only if the associated projective bundle admits an integrable holomorphic connection. A theorem by Morikawa ([3], Theorem 1) is the motivation of this problem and is somewhat strengthened by our result.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 197 - 202
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Atiyah, M. F., Complex analytic connections in fibre bundles, Trans. AMS. 85 (1957), 181–207.CrossRefGoogle Scholar
[2] Matsushima, Y., Heisenberg groups and holomorphic vector bundles over a complex torus, Nagoya Math. J. 61 (1976).CrossRefGoogle Scholar
[3] Morikawa, H., A note on holomorphic vector bundles over complex tori, Nagoya Math. J. 41 (1971), 101–106.CrossRefGoogle Scholar
[4] Weil, A., Introduction à l’étude des variétés kahleriennes, Paris, Hermann (1958).Google Scholar