Holomorphic bundles on diagonal Hopf manifolds
| dc.creator | Verbitsky, Misha | |
| dc.date | 2004-08-27 | |
| dc.date | 2004-10-11 | |
| dc.date.accessioned | 2026-07-07T07:45:32Z | |
| dc.date.available | 2026-07-07T07:45:32Z | |
| dc.description | 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. | |
| dc.description | 20 pages. Minor errors corrected in new version | |
| dc.identifier | https://arxiv.org/abs/math/0408391 | |
| dc.identifier | http://arxiv.org/abs/math/0408391 | |
| dc.identifier | Izv. Math. 70 (2006), no. 5, 13--30 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123562 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.title | Holomorphic bundles on diagonal Hopf manifolds | |
| dc.type | text |