= Twisting sheaf on projective space
{title2=$\mathcal O(d)$}
= Twisting sheaves on projective space
{synonym}
The twisting sheaf $\mathcal O(d)$ on $\operatorname{Proj}k[x_0,\ldots,x_n]$ is associated with the shifted graded module $k[x_0,\ldots,x_n](d)$. For $d\geq0$, its global sections are the homogeneous polynomials of degree $d$.
On projective space the twisting sheaf $\mathcal O(d)$ is the $d$th tensor power of $\mathcal O(1)$ for $d\geq0$, and the corresponding dual power for $d<0$. Twisting another sheaf means tensoring it with this line bundle.
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