Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T21:42:48.375Z Has data issue: false hasContentIssue false

Heisenberg groups and holomorphic vector bundles over a complex torus

Published online by Cambridge University Press:  22 January 2016

Yozo Matsushima*
Affiliation:
Department of Mathematics, University of Notre Dame
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.

Let V be a complex vector space of dimension n, L a lattice of V and E = V/L a complex torus. Let H be a Hermitian form on V. We introduce a multiplication in L × C* by

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Igusa, J., Theta functions, Springer Verlag, 1972.CrossRefGoogle Scholar
[2] Matsushima, Y., Fibres holomorphes sur un tore complexe, Nagoya Math. J. 14 (1959), 124.CrossRefGoogle Scholar
[3] Morikawa, H., A note on holomorphic vector bundles over complex tori, Nagoya Math. J. 41 (1971), 101106.CrossRefGoogle Scholar
[4] Mumford, D., Abelian varieties, Tata Inst. Studies in Math., Oxford Univ. Press, 1970.Google Scholar
[5] Oda, T., (a) Vector bundles on an elliptic curve, Nagoya Math. J. 43(1971), 4172, (b) Vector bundles on abelian surfaces, Inventions Math. 13 (1971), 247260.CrossRefGoogle Scholar
[6] Weil, A., Introduction à l’étude des variétés kahleriennes, Paris, Hermann (1958).Google Scholar
[7] Umemura, H., Some results in the theory of vector bundles, Nagoya Math. J. 52 (1973), 97128.CrossRefGoogle Scholar