A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric
نویسنده
چکیده
Let L be a local system on a smooth quasi projective variety over C . 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.
منابع مشابه
Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules
We study the asymptotic behaviour of tame harmonic bundles. First of all, we prove a local freeness of the prolongation by an increasing order. Then we obtain the polarized mixed twistor structure. As one of the applications, we obtain the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As other application, we establish the correspondence of tame harmoni...
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