Geodesic
Holomorphic bundles on diagonal Hopf manifolds
Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 867-882.

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We show that every stable holomorphic bundle on the Hopf manifold $M=(\mathbb C^n\setminus0)/\langle A\rangle$ with $\dim M\geqslant 3$, where $A\in\operatorname{GL}(n,\mathbb C)$ is a diagonal linear operator with all eigenvalues satisfying $|\alpha_i|1$, can be lifted to a $\widetilde G_F$-equivariant coherent sheaf on $\mathbb C^n$, where $\widetilde G_F\cong(\mathbb C^*)^l$ is a commutative Lie group acting on $\mathbb C^n$ and containing $A$. This is used to show that all 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 $1$. 
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M. S. Verbitsky. Holomorphic bundles on diagonal Hopf manifolds. Izvestiya. Mathematics , Tome 70 (2006) no. 5, pp. 867-882. http://geodesic.mathdoc.fr/item/IM2_2006_70_5_a1/

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