Answer by Hoot for Is a coherent locally free sheaf isomorphic it's dual?
As Jesko says, already for line bundles there are problems. The easiest example is probably $\mathscr{O}_{\mathbf{P}^n_k}(1)$ and its dual $\mathscr O(-1)$. The first has lots of nonzero global...
View ArticleIs a coherent locally free sheaf isomorphic it's dual?
Hartshorne chapter II problem 5.1 a) is to prove that the double dual of a coherent locally free sheaf $\mathscr{E}$ over a ringed space $(X,O_X)$ is isomorphic to $\mathscr{E}$. This can be done by...
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