Families of holomorphic bundles
| dc.creator | Teleman, Andrei | |
| dc.date | 2007-04-19 | |
| dc.date | 2007-05-16 | |
| dc.date.accessioned | 2026-07-07T08:01:34Z | |
| dc.date.available | 2026-07-07T08:01:34Z | |
| dc.description | The first goal of the article is to solve several fundamental problems in the theory of holomorphic bundles over non-algebraic manifolds: For instance we prove that stability and semi-stability are Zariski open properties in families when the Gauduchon degree map is a topological invariant, or when the parameter manifold is compact. Second we show that, for a generically stable family of bundles over a Kähler manifold, the Petersson-Weil form extends as a closed positive current on the whole parameter space of the family. This extension theorem uses classical tools from Yang-Mills theory developed by Donaldson (e.g. the Donaldson functional and the heat equation for Hermitian metrics on a holomorphic bundle). We apply these results to study families of bundles over a Kählerian manifold $Y$ parameterized by a non-Kählerian surface $X$, proving that such families must satisfy very restrictive conditions. These results play an important role in our program to prove existence of curves on class VII surfaces. | |
| dc.description | LaTeX, 26 pages | |
| dc.identifier | https://arxiv.org/abs/0704.2629 | |
| dc.identifier | http://arxiv.org/abs/0704.2629 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128949 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 53C55; 53C07; 32G13 | |
| dc.title | Families of holomorphic bundles | |
| dc.type | text |