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Higher cohomology of sheaves on a projective space

Let $S\subset\mathbb{P}^n$ be a finite set of $s$ reduced points. Let $\mathcal{I}$ be the ideal sheaf of $S$ in $\mathbb{P}^n$. We consider the sheaf $$\mathcal{F}_k:=\mathcal{O}_{\mathbb{P}^n}(kd)\...
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Cohomology of tangent bundles

Let $X$ be a smooth scheme and $Z\subset X$ a smooth subscheme. Consider the blow-up $$\pi:\widetilde{X}:=Bl_{Z}X\rightarrow X$$ of $X$ along $Z$. What is the relation between the cohomology of the ...
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