Holomorphic bundles on diagonal Hopf manifolds

Details Holomorphic bundles on diagonal Hopf manifolds Holomorphic bundles on diagonal Hopf manifolds

2004-08-27

arxiv.org/abs/math/0408391v2

Izv. Math. 70 (2006), no. 5, 13--30

Mathematics

Algebraic Geometry

20 pages. Minor errors corrected in new version

Scientific paper

Let $A$ be a diagonal linear operator on $\C^n$, with all eigenvalues satisfying $0<|\alpha_i|<1$, and $M = (\C^n\backslash 0)/$ 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.

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