Several complex variables and analytic spaces Analytic spaces Concept
Coherent analytic sheaf
Summary
A coherent analytic sheaf on a complex analytic space is a sheaf of modules over the structure sheaf that is locally finitely generated. Moreover, the relations among finitely many local sections must again be locally finitely generated. Coherent sheaves are the right class of sheaves for complex analytic geometry. They include the structure sheaf, ideal sheaves of analytic subsets and sheaves of sections of holomorphic vector bundles. Kernels, cokernels and images of morphisms between coherent sheaves are coherent. They are the analytic counterpart of coherent sheaves on schemes.
Where this leads
12 pages build on this one.
- Grauert's Oka principle for vector bundles
- Cartan's theorem A
- Cartan's coherence theorem for ideal sheaves
- Andreotti–Grauert theorem
- Oka's normalization theorem
- Hironaka's resolution for complex spaces
- Cartan–Serre finiteness theorem
- Grauert's semicontinuity theorem
- Oka coherence theorem
- Cartan's theorem B
- Oka principle
- Grauert's direct image theorem
Further reading
About this page
| Tag | DSJET02WPR |
|---|---|
| URI | m2://DSJET02WPR |
| Kind | concept |
| Writing | W0 stub |
| MSC | 32C35 |
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Results about this
- Cartan's theorem A
- Cartan's coherence theorem for ideal sheaves
- Cartan–Serre finiteness theorem
- Grauert's semicontinuity theorem
- Oka coherence theorem
- Cartan's theorem B
- Grauert's direct image theorem
Used by
- Cartan's theorem A
- Cartan's coherence theorem for ideal sheaves
- Andreotti–Grauert theorem
- Oka's normalization theorem
- Cartan–Serre finiteness theorem
- Grauert's semicontinuity theorem
- Oka coherence theorem
- Cartan's theorem B
- Grauert's direct image theorem