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Projective Plane Bundles Over an Elliptic Curve

Published online by Cambridge University Press:  20 November 2018

Tomokuni Takahashi
Tomokuni Takahashi*
Affiliation:
National Institute of Technology, Ichinoseki College, Ichinoseki, 021-8511, Japan, e-mail: tomokuni@ichinoseki.ac.jp
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Abstract

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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.

Keywords

14J1014J3014D15projective plane bundlevector bundleelliptic curvedeformationKodaira-Spencer map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 201 - 210
Copyright
Copyright © Canadian Mathematical Society 2018

References

[1] Atiyah, M. F., Vector bundles over an elliptic curve. Proc. London Math. Soc. (3) 7, 414–452 (1957) http://dx.doi.Org/10.1112/plms/s3-7.1.414.Google Scholar
[2] Kodaira, K., Nirenberg, L. and Spencer, D. C., On the existence of deformation of complex analytic structures. Ann. Math. 68,150–159 (1958) http://dx.doi.Org/10.2307/1970256.Google Scholar
[3] Kodaira, K. and Spencer, D. C., A theorem of completeness for complex analytic fiber Spaces. Acta Math. 100, 281–294(1958) http://dx.doi.org/10.1007/BF02559541.Google Scholar
[4] Suwa, T., On ruled surfaces ofgenus 1. J. Math. Soc. Japan 21, 291–311 (1969) http://dx.doi.org/10.2969/jmsj702120291Google Scholar