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