Nonabelian Hodge theory for Fujiki class $\mathcal C$ manifolds

TL;DR

This paper extends the nonabelian Hodge correspondence, linking polystable Higgs bundles and flat connections, to a broader class of complex manifolds known as Fujiki class $ ext{C}$, beyond compact Kähler manifolds.

Contribution

It generalizes the nonabelian Hodge theory to Fujiki class $ ext{C}$ manifolds, broadening its applicability in complex geometry.

Findings

Established the correspondence for Fujiki class $ ext{C}$ manifolds.

Extended the scope of nonabelian Hodge theory beyond Kähler manifolds.

Provided new tools for studying complex manifolds in this class.

Abstract

The nonabelian Hodge correspondence (Corlette-Simpson correspondence), between the polystable Higgs bundles with vanishing Chern classes on a compact K\"ahler manifold $X$ and the completely reducible flat connections on $X$, is extended to the Fujiki class $\mathcal C$ manifolds.