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Projective Plane Bundles Over an Elliptic Curve

  • Tomokuni Takahashi (a1)
Abstract

We calculate the dimension of cohomology groups for the holomorphic tangent bundles of each isomorphism class of the projective plane bundle over an elliptic curve. As an application, we construct the families of projective plane bundles, and prove that the families are effectively parametrized and complete.

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[1] Atiyah, M. F., Vector bundles over an elliptic curve. Proc. London Math. Soc. (3) 7, 414452 (1957) http://dx.doi.Org/10.1112/plms/s3-7.1.414.
[2] Kodaira, K., Nirenberg, L. and Spencer, D. C., On the existence of deformation of complex analytic structures. Ann. Math. 68,150159 (1958) http://dx.doi.Org/10.2307/1970256.
[3] Kodaira, K. and Spencer, D. C., A theorem of completeness for complex analytic fiber Spaces. Acta Math. 100, 281294(1958) http://dx.doi.org/10.1007/BF02559541.
[4] Suwa, T., On ruled surfaces ofgenus 1. J. Math. Soc. Japan 21, 291311 (1969) http://dx.doi.org/10.2969/jmsj702120291
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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