∂¯-tangential invariants of certain vector bundles over complex foliations

Stable Approximations of Certain Vector Bundles

0 −−−−→ O s −−−−→ E0 s∗ −−−−→ I −−−−→ 0. As usual, s is the distinguished nonzero global section of E0. The determinant line bundle of E0 is trivial, while the second Chern class is equal to the integer k. If X is in particular an algebraic surface, and H a fixed ample line bundle, then we can talk about slope-stability with respect to H. The bundle E0 is only slopesemistable, of slope 0, but t...

Classification of Equivariant Complex Vector Bundles over a Circle

In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the extensions of representations. As a corollary of our results, we calculate the reduced equivariant K-group of a circle for any compact Lie group.

Notes on homogeneous vector bundles over complex flag manifolds

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset Σ of simple roots of G, and let Eφ be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation φ of P . Using Bott’s theorem, we obtain sufficient conditions on φ in terms of the combinatorial structure of Σ for some cohomology groups of the sheaf of holomorphic sections ...

Vector bundles over algebraic curves

Rigidity of Certain Holomorphic Foliations

There is a well-known rigidity theorem of Y. Ilyashenko for (singular) holomorphic foliations in CP and also the extension given by Gómez-Mont and Ort́ız-Bobadilla (1989). Here we present a different generalization of the result of Ilyashenko: some cohomological and (generic) dynamical conditions on a foliation F on a fibred complex surface imply the d-rigidity of F , i.e. any topologically triv...