Stable bundles on positive principal elliptic fibrations
| dc.creator | Verbitsky, Misha | |
| dc.date | 2004-03-25 | |
| dc.date.accessioned | 2026-07-07T06:22:23Z | |
| dc.date.available | 2026-07-07T06:22:23Z | |
| dc.description | Let $M\stackrelπ\arrow X$ be a principal elliptic fibration over a Kaehler base $X$. We assume that the Kaehler form on $X$ is lifted to an exact form on $M$ (such fibrations are called positive). Examples of these are regular Vaisman manifolds (in particular, the regular Hopf manifolds) and Calabi-Eckmann manifolds. Assume that $\dim M > 2$. Using the Kobayashi-Hitchin correspondence, we prove that all stable bundles on $M$ are flat on the fibers of the elliptic fibration. This is used to show that all stable vector bundles on $M$ take form $L\otimes π^* B_0$, where $B_0$ is a stable bundle on $X$, and $L$ a holomorphic line bundle. For $X$ algebraic this implies that all holomorphic bundles on $M$ are filtrable (that is, obtained by successive extensions of rank-1 sheaves). We also show that all positive-dimensional compact subvarieties of $M$ are pullbacks of complex subvarieties on $X$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0403430 | |
| dc.identifier | http://arxiv.org/abs/math/0403430 | |
| dc.identifier | Math. Res. Lett. 12 (2005), no. 2-3, 251--264. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95892 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.title | Stable bundles on positive principal elliptic fibrations | |
| dc.type | text |