= Dual of a sheaf
{title2=$\mathcal F^\vee=\mathcal H om_{\mathcal O_X}(\mathcal F,\mathcal O_X)$}
The dual is the <sheaf of modules> whose sections on $U$ are module-sheaf morphisms $\mathcal F|_U\to\mathcal O_U$. For a <locally free sheaf> of finite rank, the dual is locally free of the same rank and the natural double-dual map is an isomorphism. General <coherent sheaves> need not have this property: a skyscraper at a point of positive-dimensional projective space has zero ordinary sheaf dual.
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