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Projective plane bundles over an elliptic curve

Published:2017-06-07
Printed: Mar 2018
• Tomokuni Takahashi,
National Institute of Technology, Ichinoseki College, Ichinoseki, 021-8511, Japan
 Format: LaTeX MathJax PDF

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.
 Keywords: projective plane bundle, vector bundle, elliptic curve, deformation, Kodaira-Spencer map
 MSC Classifications: 14J10 - Families, moduli, classification: algebraic theory 14J30 - $3$-folds [See also 32Q25] 14D15 - Formal methods; deformations [See also 13D10, 14B07, 32Gxx]

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