Lefschetz principle-type theorems for curve semistable Higgs sheaves and applications to elliptic surfaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915942460555264 |
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| author | Capasso, Armando |
| author_facet | Capasso, Armando |
| contents | I prove "Lefschetz principle"-type theorems for semistable and curve semistable Higgs sheaves on smooth projective varieties defined over an algebraically closed field of characteristic $0$. These theorems are applied to reduce a conjecture, about curve semistable Higgs bundles, from the previous general setting to the complex case. Since this conjecture is equivalent to vanishing of Chern classes of H-nflat Higgs bundles, I consider these last ones over elliptic surfaces. I reduce one more time the conjecture to nilpotent, H-nflat Higgs bundles, and I prove it on elliptic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00439 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lefschetz principle-type theorems for curve semistable Higgs sheaves and applications to elliptic surfaces Capasso, Armando Algebraic Geometry 14A10, 14A15, 14F06, 14J27, 14J60 I prove "Lefschetz principle"-type theorems for semistable and curve semistable Higgs sheaves on smooth projective varieties defined over an algebraically closed field of characteristic $0$. These theorems are applied to reduce a conjecture, about curve semistable Higgs bundles, from the previous general setting to the complex case. Since this conjecture is equivalent to vanishing of Chern classes of H-nflat Higgs bundles, I consider these last ones over elliptic surfaces. I reduce one more time the conjecture to nilpotent, H-nflat Higgs bundles, and I prove it on elliptic surfaces. |
| title | Lefschetz principle-type theorems for curve semistable Higgs sheaves and applications to elliptic surfaces |
| topic | Algebraic Geometry 14A10, 14A15, 14F06, 14J27, 14J60 |
| url | https://arxiv.org/abs/2412.00439 |