A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric
| dc.creator | Mochizuki, Takuro | |
| dc.date | 2004-02-08 | |
| dc.date.accessioned | 2026-07-07T05:05:14Z | |
| dc.date.available | 2026-07-07T05:05:14Z | |
| dc.description | Let $L$ be a local system on a smooth quasi projective variety over $\cnum$. We see that $L$ is semisimple if and only if there exists a tame pure imaginary pluri-harmonic metric on $L$. Although it is a rather minor refinement of a result of Jost and Zuo, it is significant for the study of harmonic bundles and pure twistor $D$-modules. As one of the application, we show that the semisimplicity of local systems are preserved by the pull back via a morphism of quasi projective varieties. This paper will be included as an appendix to our previous paper, ``Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules'', math.DG/0312230. Keywords: Higgs fields, harmonic bundle, semisimple local system. | |
| dc.identifier | https://arxiv.org/abs/math/0402122 | |
| dc.identifier | http://arxiv.org/abs/math/0402122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70096 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53C07, 53C43, 53C55 | |
| dc.title | A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric | |
| dc.type | text |