Holomorphic bundles on diagonal Hopf manifolds
نویسنده
چکیده
Let A ∈ GL(n,C) be a diagonal linear operator, with all eigenvalues satisfying |αi| < 1, and M = (Cn\0)/〈A〉 the corresponding Hopf manifold. We show that any stable holomorphic bundle on M can be lifted to a G̃F equivariant coherent sheaf on C, where G̃F ∼= (C) is a commutative Lie group acting on C and containing A. This is used to show that all stable bundles onM are filtrable, that is, admit a filtration by a sequence Fi of coherent sheaves, with all subquotients Fi/Fi−1 of rank 1.
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