Harder-Narasimhan filtrations of decorated vector bundles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918365501587456 |
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| author | Roth, Emanuel Schaffhauser, Florent |
| author_facet | Roth, Emanuel Schaffhauser, Florent |
| contents | A decorated vector bundle is a vector bundle equipped with a reduction of structure group to a complex reductive subgroup $G \subseteq \mathbf{GL}(r,\mathbb{C})$. Examples include symplectic and special-orthogonal vector bundles, as well as vector bundles with trivial determinants. In this expository paper, we provide direct constructions of Harder-Narasimhan filtrations of symplectic and special-orthogonal vector bundles, and use them to construct canonical reductions in the sense of Atiyah and Bott. We compare these canonical reductions to those constructed by Biswas and Holla. Lastly, we set up the obstruction theory necessary to define Harder-Narasimhan types of principal bundles, and stratify the moduli stack of principal $G$-bundles. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17371 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harder-Narasimhan filtrations of decorated vector bundles Roth, Emanuel Schaffhauser, Florent Algebraic Geometry 14D20 A decorated vector bundle is a vector bundle equipped with a reduction of structure group to a complex reductive subgroup $G \subseteq \mathbf{GL}(r,\mathbb{C})$. Examples include symplectic and special-orthogonal vector bundles, as well as vector bundles with trivial determinants. In this expository paper, we provide direct constructions of Harder-Narasimhan filtrations of symplectic and special-orthogonal vector bundles, and use them to construct canonical reductions in the sense of Atiyah and Bott. We compare these canonical reductions to those constructed by Biswas and Holla. Lastly, we set up the obstruction theory necessary to define Harder-Narasimhan types of principal bundles, and stratify the moduli stack of principal $G$-bundles. |
| title | Harder-Narasimhan filtrations of decorated vector bundles |
| topic | Algebraic Geometry 14D20 |
| url | https://arxiv.org/abs/2511.17371 |