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Bibliographic Details
Main Authors: Dimakis, Panagiotis, Schulz, Sebastian
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.12945
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Table of Contents:
  • On a compact Riemann surface $Σ$ of genus $g>1$, equipped with a complex vector bundle $E$ of rank $2$ and degree zero let $M_H$ be the moduli space of Higgs bundles. $M_H$ admits a $\mathbb C^{\star}$-action and to each stable $\mathbb C^{\star}$-fixed point $[(\bar\partial_0,Φ_0)]$ is associated a holomorphic Lagrangian submanifold $W^1(\bar\partial_0,Φ_0)$ inside the de Rham moduli space $M_{dR}$ of complex flat connections. In this note we prove a conjecture of Simpson stating that $W^1(\bar\partial_0,Φ_0)$ is closed inside $M_{dR}$.