arXiv subjects

Quoc-Anh Tran

Publications and source records attributed to Quoc-Anh Tran.

3 recordsLinked to original sources

arXiv2026

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

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.

math.AG↗

arXiv2026

Perverse Euler Characteristics of Hermitian Locally Symmetric Spaces

We prove that finite-volume locally Hermitian symmetric spaces of noncompact type have nonnegative perverse Euler characteristics. To show this, we obtain a nefness result for the logarithmic cotangent bundle of a smooth toroidal compactification. Combining this with a positivity criterion for Euler characteristics of perverse sheaves, we deduce the nonnegativity result. We further prove that the inequality is strict for perverse sheaves with full support. As applications, we get nonnegativity results for perverse Euler characteristics on various moduli spaces.

math.AG↗

arXiv2026

On the nilpotent residue non-abelian Hodge correspondence for higher-dimensional quasiprojective varieties

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.

math.AG↗