On the nilpotent residue non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915746582364160 |
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| author | Tran, Quoc-Anh |
| author_facet | Tran, Quoc-Anh |
| contents | In arXiv:2408.16441, the authors proved that on a projective log smooth variety $(\bar{X}, D)$ there is a continuous bijection between the moduli space $M^{\mathrm{nilp}}_{\mathrm{Dol}}(\bar{X}, D)$ of logarithmic Higgs bundles with nilpotent residues and the moduli space $M^{\mathrm{nilp}}_{\mathrm{DR}}(\bar{X}, D)$ of logarithmic connections with nilpotent residues. In this note, we argue that the map is a homeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the nilpotent residue non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties Tran, Quoc-Anh Algebraic Geometry In arXiv:2408.16441, the authors proved that on a projective log smooth variety $(\bar{X}, D)$ there is a continuous bijection between the moduli space $M^{\mathrm{nilp}}_{\mathrm{Dol}}(\bar{X}, D)$ of logarithmic Higgs bundles with nilpotent residues and the moduli space $M^{\mathrm{nilp}}_{\mathrm{DR}}(\bar{X}, D)$ of logarithmic connections with nilpotent residues. In this note, we argue that the map is a homeomorphism. |
| title | On the nilpotent residue non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.15553 |