Equivariant principal bundles over the complex projective line

On Semistable Principal Bundles over a Complex Projective Manifold, Ii

Let (X, ω) be a compact connected Kähler manifold of complex dimension d and EG −→ X a holomorphic principal G–bundle, where G is a connected reductive linear algebraic group defined over C. Let Z(G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P ⊂ G and a holomorphic reduction of structure group EP ⊂ EG to P , such that ...

On Semistable Principal Bundles over a Complex Projective Manifold

Let G be a simple linear algebraic group defined over the field of complex numbers. Fix a proper parabolic subgroup P of G, and also fix a nontrivial antidominant character χ of P . We prove that a holomorphic principal G–bundle EG over a connected complex projective manifold M is semistable satisfying the condition that the second Chern class c2(ad(EG)) ∈ H (M, Q) vanishes if and only if the l...

Equivariant Principal Bundles over Spheres and Cohomogeneity One Manifolds

We classify SO(n)-equivariant principal bundles over Sn in terms of their isotropy representations over the north and south poles. This is an example of a general result classifying equivariant (Π, G)-bundles over cohomogeneity one manifolds.

The Equivariant Brauer Groups of Principal Bundles

A Remark on the Jet Bundles over the Projective Line

Let X be a Riemann surface equipped with a projective structure (i.e., a covering by coordinate charts such that the transition functions are of the form z 7−→ (az + b)/(cz + d)). Let L be a line bundle on X such that L = TX . Let J (L) −→ X denote the jet bundle of order m for the line bundle L. For i ≥ j, there is a natural restriction homomorphism from J (L) onto J (L). We prove that for any...