Abstract
Let
A
be a diagonal linear operator on $\C^n$, with all eigenvalues satisfying
0<|
α
i
|<1
, and $M = (\C^n\backslash 0)/<A>$ the corresponding Hopf manifold. We show that any stable holomorphic bundle on
M
can be lifted to a
G
-equivariant coherent sheaf on $\C^n$, where $G=(\C^*)^l$ is a Lie group acting on $\C^n$ and containing
A
. This is used to show that all stable bundles on
M
are filtrable, that is, admit a filtration by a sequence
F
i
of coherent sheaves, with all subquotients
F
i
/
F
i−1
of rank 1.