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arXiv · 2506.04094

Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$

Anna-Maria Raukh
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Abstract

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 $i^*$.

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Anna-Maria Raukh. 2025-06-04. Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$. https://arxiv.org/abs/2506.04094

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