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How to compute cohomology groups of a closed subscheme Z of projective space, defined by a homogeneous polynomial of degree d?
Let $Z = \mathrm{Proj}\,k[x_{0},x_{1},\ldots,x_{r}]/f$ be a closed subscheme of degree $d$, i.e., $f$ is a homogeneous polynomial of degree $d$, and $\mathcal{O}_{Z}(1)=i^{*}\mathcal{O}_\mathbb{P}(1)$....
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