Nonabelian Hodge theory for Fujiki class \(\mathcal{C}\) manifolds. (English) Zbl 1510.32025
Summary: The nonabelian Hodge correspondence (also known as the Corlette-Simpson correspondence), between the polystable Higgs bundles with vanishing Chern classes on a compact Kähler manifold \(X\) and the completely reducible flat connections on \(X\), is extended to the Fujiki class \(\mathcal{C}\) manifolds.
MSC:
| 32G13 | Complex-analytic moduli problems |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 58D27 | Moduli problems for differential geometric structures |
| 14E05 | Rational and birational maps |
Keywords:
nonabelian Hodge theory; flat connection; Higgs bundle; Fujiki class; \(\mathcal{C}\) manifoldReferences:
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