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arXiv · 2601.13071

Non-abelian Hodge correspondence over singular Kähler spaces

Chuanjing Zhang·Shiyu Zhang·Xi Zhang
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Abstract

In this paper, we establish the non-abelian Hodge correspondence over compact Kähler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, thereby extending the result of Greb-Kebekus-Peternell-Taji for projective klt varieties to the context of compact Kähler klt spaces. The proof relies on two key ingredients: first, we establish an equivalence over the regular loci-via harmonic bundles-between polystable Higgs bundles with vanishing orbifold Chern numbers and semi-simple flat bundles; second, we prove a descent theorem for semistable Higgs bundles with vanishing Chern classes along resolutions of singularities. As an application of our framework, we obtain a quasi-uniformization theorem for projective klt varieties with big canonical divisor that satisfy the orbifold Miyaoka-Yau equality.

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Chuanjing Zhang, Shiyu Zhang, Xi Zhang. 2026-03-06. Non-abelian Hodge correspondence over singular Kähler spaces. https://arxiv.org/abs/2601.13071

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