Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913875151028224 |
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| author | Raukh, Anna-Maria |
| author_facet | Raukh, Anna-Maria |
| contents | Given a hypersurface $i \colon X \hookrightarrow \widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \mathbb{Z})^{\otimes n-1} \to \mathbb{Z}$ for the purpose of identifying Fano manifolds obtained from smoothing singular Fanos. In the process, we describe the integer cohomology groups $H^k(X, \mathbb{Z})$ for $k<n$ and give an explicit formula for the pullback map $i^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$ Raukh, Anna-Maria Algebraic Geometry Algebraic Topology Given a hypersurface $i \colon X \hookrightarrow \widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \mathbb{Z})^{\otimes n-1} \to \mathbb{Z}$ for the purpose of identifying Fano manifolds obtained from smoothing singular Fanos. In the process, we describe the integer cohomology groups $H^k(X, \mathbb{Z})$ for $k<n$ and give an explicit formula for the pullback map $i^*$. |
| title | Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$ |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2506.04094 |