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Holomorphically Convex Domains and the Oka–Cartan Fundamental Theorem

In: Analytic Function Theory of Several Variables

Author

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  • Junjiro Noguchi

    (The University of Tokyo
    Tokyo Institute of Technology)

Abstract

In this chapter we prove the Oka–Cartan Fundamental Theorem on holomorphically convex domain $$\varOmega $$ of $${\textbf{C}}^n$$ ; that, is, it is proved that $$H^q(\varOmega , \mathscr {F})=0$$ ( $$q \ge 1$$ ) for every coherent sheaf $$\mathscr {F}$$ over holomorphically convex domains $$\varOmega $$ . In the course of the proof, Oka’s Jôku-Ikô plays an essential role.

Suggested Citation

  • Junjiro Noguchi, 2016. "Holomorphically Convex Domains and the Oka–Cartan Fundamental Theorem," Springer Books, in: Analytic Function Theory of Several Variables, chapter 0, pages 111-153, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-0291-5_4
    DOI: 10.1007/978-981-10-0291-5_4
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