Twisted Higgs bundles and the fundamental group of compact Kähler manifolds. (English) Zbl 1003.53026
The authors consider polystable Higgs bundles twisted by a holomorphic line bundle \(L\) over a compact Kähler manifold \(X\), with vanishing first and second Chern classes of the bundle. The case \(\deg L=0\) and \(L^n \cong\) trivial bundle for some \(n\in\mathbb{N}\) is treated. Then \(L\) corresponds to a unitary character \(\pi_1(X)\to U(1)\) of the fundamental group of \(X\). This is used to identify the corresponding Tannaka group in terms of the pro-reductive completion of \(\pi_1(X)\).
Reviewer: Alfred Aeppli (Minneapolis)
MSC:
53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
32L25 | Twistor theory, double fibrations (complex-analytic aspects) |