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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.12945 |
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| _version_ | 1866910653968547840 |
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| author | Dimakis, Panagiotis Schulz, Sebastian |
| author_facet | Dimakis, Panagiotis Schulz, Sebastian |
| 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 $M_{dR}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a conjecture of Simpson Dimakis, Panagiotis Schulz, Sebastian Differential Geometry 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 $M_{dR}$. |
| title | On a conjecture of Simpson |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.12945 |