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Cohomology of the tangent sheaf of $\mathbb{P}(1,2,3)$
Using the exact sequence
$$0\mapsto\mathcal{O}_{\mathbb{P}^{2}}\rightarrow\mathcal{O}_{\mathbb{P}^{2}}(1)^{\oplus 3}\rightarrow T_{\mathbb{P}^{2}}\mapsto 0$$
it is easy to compute $H^{1}(\mathbb{P}^...
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