An h-principle for complements of discriminants
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910996630601728 |
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| author | Aumonier, Alexis |
| author_facet | Aumonier, Alexis |
| contents | We compare spaces of non-singular algebraic sections of ample vector bundles to spaces of continuous sections of jet bundles. Under some conditions, we provide an isomorphism in homology in a range of degrees growing with the jet ampleness. As an application, when $\mathcal{L}$ is a very ample line bundle on a smooth projective complex variety, we prove that the rational cohomology of the space of non-singular algebraic sections of $\mathcal{L}^{\otimes d}$ stabilises as $d \to \infty$ and compute the stable cohomology. We also prove that the integral homology does not stabilise using tools from stable homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_00326 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An h-principle for complements of discriminants Aumonier, Alexis Algebraic Topology Algebraic Geometry 55R80 (Primary), 14J10, 14J70 (Secondary) We compare spaces of non-singular algebraic sections of ample vector bundles to spaces of continuous sections of jet bundles. Under some conditions, we provide an isomorphism in homology in a range of degrees growing with the jet ampleness. As an application, when $\mathcal{L}$ is a very ample line bundle on a smooth projective complex variety, we prove that the rational cohomology of the space of non-singular algebraic sections of $\mathcal{L}^{\otimes d}$ stabilises as $d \to \infty$ and compute the stable cohomology. We also prove that the integral homology does not stabilise using tools from stable homotopy theory. |
| title | An h-principle for complements of discriminants |
| topic | Algebraic Topology Algebraic Geometry 55R80 (Primary), 14J10, 14J70 (Secondary) |
| url | https://arxiv.org/abs/2112.00326 |