PreprintCC BY 4.0arXiv
The non-abelian Hodge correspondence for extensions on quasi-projective curves
Abstract
Let X̅ be a smooth projective connected complex curve, D ⊂ X̅ be a finite set of reduced points, and X=X̅∖ D. We give a moduli-theoretic construction of an exact equivalence between logarithmic flat bundles on (X̅, D) with nilpotent residues and semistable logarithmic Higgs bundles of degree zero with nilpotent residues. This extends the tame Simpson-Mochizuki correspondence on polystable bundles.
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BibTeX
@misc{tran2026nonabelian,
title = {{The non-abelian Hodge correspondence for extensions on quasi-projective curves}},
author = {Quoc-Anh Tran},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26896},
eprint = {2609.26896},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26896},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The non-abelian Hodge correspondence for extensions on quasi-projective curves
AU - Quoc-Anh Tran
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26896
UR - https://arxiv.org/abs/2609.26896
AB - Let X̅ be a smooth projective connected complex curve, D ⊂ X̅ be a finite set of reduced points, and X=X̅∖ D. We give a moduli-theoretic construction of an exact equivalence between logarithmic flat bundles on (X̅, D) with nilpotent residues and semistable logarithmic Higgs bundles of degree zero with nilpotent residues. This extends the tame Simpson-Mochizuki correspondence on polystable bundles.
ER -