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twisting sheaves
\begin{align*} {\mathcal{O}}_{{\mathbf{P}}^n}(d)(U) \to \left\{{g/f {~\mathrel{\Big\vert}~}g\in k[x_1, \cdots, x_{n}]_e, f\in k[x_1, \cdots, x_{n}]_{e+d} , f(p)\neq 0 \,\, \forall p\in U}\right\} \end{align*}
\begin{align*} {\mathcal{O}}_{{\mathbf{P}}^n}(d)(U) \to \left\{{g/f {~\mathrel{\Big\vert}~}g\in k[x_1, \cdots, x_{n}]_e, f\in k[x_1, \cdots, x_{n}]_{e+d} , f(p)\neq 0 \,\, \forall p\in U}\right\} \end{align*}