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arXiv · 2609.26896

The non-abelian Hodge correspondence for extensions on quasi-projective curves

Quoc-Anh Tran
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Abstract

Let $\bar{X}$ be a smooth projective connected complex curve, $D \subset \bar X$ be a finite set of reduced points, and $X=\bar X\setminus D$. We give a moduli-theoretic construction of an exact equivalence between logarithmic flat bundles on $(\bar X, D)$ 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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Quoc-Anh Tran. 2026-09-22. The non-abelian Hodge correspondence for extensions on quasi-projective curves. https://arxiv.org/abs/2609.26896

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