Non-abelian Hodge correspondence over singular Kähler spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908869865766912 |
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| author | Zhang, Chuanjing Zhang, Shiyu Zhang, Xi |
| author_facet | Zhang, Chuanjing Zhang, Shiyu Zhang, Xi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13071 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-abelian Hodge correspondence over singular Kähler spaces Zhang, Chuanjing Zhang, Shiyu Zhang, Xi Differential Geometry Algebraic Geometry Complex Variables 32J25, 32J27, 53C07 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. |
| title | Non-abelian Hodge correspondence over singular Kähler spaces |
| topic | Differential Geometry Algebraic Geometry Complex Variables 32J25, 32J27, 53C07 |
| url | https://arxiv.org/abs/2601.13071 |