Chern numbers on positive vector bundles and combinatorics
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915415413751808 |
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| author | Li, Ping |
| author_facet | Li, Ping |
| contents | Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards a long-standing question. Along this line we prove that Chern numbers on nef vector bundles obey reverse dominance ordering, which improves upon some classical and recent results. We propose a simultaneous positivity question on (signed) Chern numbers of compact complex or Kähler manifolds whose (co)tangent bundles are semipositive in various senses, and show that it holds true for compact homogeneous complex manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern numbers on positive vector bundles and combinatorics Li, Ping Differential Geometry Algebraic Geometry Combinatorics 32Q55, 57R20, 06A07, 32M10 Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards a long-standing question. Along this line we prove that Chern numbers on nef vector bundles obey reverse dominance ordering, which improves upon some classical and recent results. We propose a simultaneous positivity question on (signed) Chern numbers of compact complex or Kähler manifolds whose (co)tangent bundles are semipositive in various senses, and show that it holds true for compact homogeneous complex manifolds. |
| title | Chern numbers on positive vector bundles and combinatorics |
| topic | Differential Geometry Algebraic Geometry Combinatorics 32Q55, 57R20, 06A07, 32M10 |
| url | https://arxiv.org/abs/2501.08833 |