An overview on curve semistable and numerically flat Higgs bundles
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911343645294592 |
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| author | Capasso, Armando |
| author_facet | Capasso, Armando |
| contents | After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these latter can be used to define generalisations of the notion of positivity conditions, such as numerically flatness, which "feel" the Higgs field. Then I prove several properties of Higgs bundles, over smooth projective varieties defined over an algebraically closed field of characteristic $0$, satisfying these conditions. Finally, I discuss how one can relate them to semistability of the so-called "curve semistable" Higgs bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An overview on curve semistable and numerically flat Higgs bundles Capasso, Armando Algebraic Geometry 14A15, 14F06, 14H60, 14J60 After recalling the basic notions concerning Higgs-Grassmannian schemes, I review how these latter can be used to define generalisations of the notion of positivity conditions, such as numerically flatness, which "feel" the Higgs field. Then I prove several properties of Higgs bundles, over smooth projective varieties defined over an algebraically closed field of characteristic $0$, satisfying these conditions. Finally, I discuss how one can relate them to semistability of the so-called "curve semistable" Higgs bundles. |
| title | An overview on curve semistable and numerically flat Higgs bundles |
| topic | Algebraic Geometry 14A15, 14F06, 14H60, 14J60 |
| url | https://arxiv.org/abs/2512.23529 |