A Hitchin-Kobayashi correspondence for Kaehler fibrations
| dc.creator | Riera, Ignasi Mundet i | |
| dc.date | 1999-01-19 | |
| dc.date | 1999-11-17 | |
| dc.date.accessioned | 2026-07-07T05:27:35Z | |
| dc.date.available | 2026-07-07T05:27:35Z | |
| dc.description | Let $X$ be a compact Kaehler manifold and $E\to X$ a principal $K$ bundle, where $K$ is a compact connected Lie group. Let ${\cal A}^{1,1}$ be the set of connections on $E$ whose curvature lies in $Ω^{1,1}(E\times_{Ad} {\frak k})$, where ${\frak k}$ is the Lie algebra of $K$. Endow $\frak k$ with a nondegenerate biinvariant bilinear pairing. This allows to identify $\{\frak k}\simeq{\frak k}^*$. Let $F$ be a Kaehler left $K$-manifold and suppose that there exists a moment map $μ$ for the action of $K$ on $F$. Let ${\cal S}=Γ(E\times_K F)$. In this paper we study the equation $$ΛF_A+μ(Φ)=c$$ for $A\in {\cal A}^{1,1}$ and a section $Φ\in {\cal S}$, where $c\in{\frak k}$ is a fixed central element. We study which orbits of the action of the complex gauge group on ${cal A}^{1,1}\times{\cal S}$ contain solutions of the equation, and we define a positive functional on ${cal A}^{1,1}\times{\cal S}$ which generalises the Yang-Mills-Higgs functional and whose local minima coincide with the solutions of the equation. | |
| dc.description | 41 pages, no figures, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/9901076 | |
| dc.identifier | http://arxiv.org/abs/math/9901076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77971 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53C07; 32L07; 35Q40 | |
| dc.title | A Hitchin-Kobayashi correspondence for Kaehler fibrations | |
| dc.type | text |