Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Quoc-Anh Tran

Abstract

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.

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

Abstract

In arXiv:2408.16441, the authors proved that on a projective log smooth variety there is a continuous bijection between the moduli space of logarithmic Higgs bundles with nilpotent residues and the moduli space of logarithmic connections with nilpotent residues. In this note, we argue that the map is a homeomorphism.
Paper Structure (1 section, 4 theorems, 10 equations)

This paper contains 1 section, 4 theorems, 10 equations.

Table of Contents

  1. Acknowledgement

Key Result

Theorem 1

There exists a Lefschetz curve $\bar{C} \subset \bar{X}$ so that the restriction map $i_{\mathrm{Dol}}^*$ is proper.

Theorems & Definitions (11)

  • Definition
  • Theorem 1
  • Corollary 2
  • Definition
  • Proposition 3
  • proof
  • Proposition 4
  • proof
  • Claim 5
  • proof : Proof of claim
  • ...and 1 more