Strong semistability of Higgs bundles over curves
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911561030828032 |
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| author | Liu, Bowen Sheng, Mao |
| author_facet | Liu, Bowen Sheng, Mao |
| contents | In this paper we complete the study of the Lan-Sheng-Zuo conjecture proposed in arXiv:1210.8280 for the curve case. Precisely, we prove that every semistable Higgs bundle is strongly semistable for curves of genus $g\leq 1$, and over any curves of genus $g\ge2$ construct explicit examples of semistable Higgs bundles of arbitrary big rank (the first example is $p=2,r=3$) which are not strongly semistable. These results are complementary to the strongly semistability theorem of Lan-Sheng-Yang-Zuo and Langer for semistable Higgs bundles of small rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15142 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong semistability of Higgs bundles over curves Liu, Bowen Sheng, Mao Algebraic Geometry 14H60 In this paper we complete the study of the Lan-Sheng-Zuo conjecture proposed in arXiv:1210.8280 for the curve case. Precisely, we prove that every semistable Higgs bundle is strongly semistable for curves of genus $g\leq 1$, and over any curves of genus $g\ge2$ construct explicit examples of semistable Higgs bundles of arbitrary big rank (the first example is $p=2,r=3$) which are not strongly semistable. These results are complementary to the strongly semistability theorem of Lan-Sheng-Yang-Zuo and Langer for semistable Higgs bundles of small rank. |
| title | Strong semistability of Higgs bundles over curves |
| topic | Algebraic Geometry 14H60 |
| url | https://arxiv.org/abs/2505.15142 |