Examples of Coherent Sheaves
- On noetherian schemes, the structure sheaf itself.
- Sheaves of sections in vector bundles.
- The Oka coherence theorem shows that the sheaf of holomorphic functions on a complex manifold is coherent.
- Ideal sheaves: If Z is a closed complex subspace of a complex analytic space X, the sheaf IZ of all holomorphic functions vanishing on Z is coherent.
- Structure sheaves of subspaces.
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