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Restriction of the sheaf of relative differentials

Let $f:X\rightarrow C$ be a morphism, where $C$ is a smooth curve, and let $\Omega_f$ be the sheaf of relative differentials. For $t\in C$ let $i_t:X_t = f^{-1}(t)\rightarrow X$ be the inclusion of ...
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A question about the sheaf supported on the zero section

Let $X$ be the total space of the cotangent sheaf on $\mathbb{P}^{2}$ and $i \colon \mathbb{P}^{2} \hookrightarrow X$ be thezero section. Suppose that $E$ is a coherent sheaf on $X$ which is set-...
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