Poincar{é} Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911226786742272 |
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| author | Chenal, Jules |
| author_facet | Chenal, Jules |
| contents | In this article, we present two structural results about the Renaudineau-Shaw spectral sequence that computes the cohomology of T-hypersurfaces. The first is a Poincar{é} duality satisfied by all its pages of positive index. The second is a vanishing criterion. It reformulates the vanishing of the boundary operators of the spectral sequence as the injectivity of some morphisms induced in cohomology by the inclusion of the T-hypersurface in its surrounding toric variety. It implies that the Renaudineau-Shaw spectral sequence of a T-hypersurface degenerates at the second page if and only if the T-hypersurface satisfies a real version of the Lefschetz Hyperplane Section Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11919 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Poincar{é} Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces Chenal, Jules Algebraic Geometry Algebraic Topology In this article, we present two structural results about the Renaudineau-Shaw spectral sequence that computes the cohomology of T-hypersurfaces. The first is a Poincar{é} duality satisfied by all its pages of positive index. The second is a vanishing criterion. It reformulates the vanishing of the boundary operators of the spectral sequence as the injectivity of some morphisms induced in cohomology by the inclusion of the T-hypersurface in its surrounding toric variety. It implies that the Renaudineau-Shaw spectral sequence of a T-hypersurface degenerates at the second page if and only if the T-hypersurface satisfies a real version of the Lefschetz Hyperplane Section Theorem. |
| title | Poincar{é} Duality, Degeneracy, and Real Lefschetz Property for T-Hypersurfaces |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2312.11919 |