Constructing Parabolic Non-Abelian Hodge Correspondence in Positive Characteristic Using Parabolic Bases
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909464563548160 |
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| author | Lin, Xiaojin |
| author_facet | Lin, Xiaojin |
| contents | We introduce the concept of parabolic bases to establish a localized framework for parabolic bundles and parabolic $λ$-connections. Building on this foundation, we propose a novel method for constructing the parabolic non-abelian Hodge correspondence in positive characteristic, extending the work originally developed by Krishnamoorthy and Sheng for algebraic curves. Additionally, we investigate the rank $2$ parabolic Higgs-de Rham flow operator and present a modified version of the Sun-Yang-Zuo algorithm, specifically adapted to the parabolic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Parabolic Non-Abelian Hodge Correspondence in Positive Characteristic Using Parabolic Bases Lin, Xiaojin Algebraic Geometry 14A21, 14G17 (primary), 14H30, 14J60, 14H60 We introduce the concept of parabolic bases to establish a localized framework for parabolic bundles and parabolic $λ$-connections. Building on this foundation, we propose a novel method for constructing the parabolic non-abelian Hodge correspondence in positive characteristic, extending the work originally developed by Krishnamoorthy and Sheng for algebraic curves. Additionally, we investigate the rank $2$ parabolic Higgs-de Rham flow operator and present a modified version of the Sun-Yang-Zuo algorithm, specifically adapted to the parabolic setting. |
| title | Constructing Parabolic Non-Abelian Hodge Correspondence in Positive Characteristic Using Parabolic Bases |
| topic | Algebraic Geometry 14A21, 14G17 (primary), 14H30, 14J60, 14H60 |
| url | https://arxiv.org/abs/2501.13775 |