Cohomology of Coherent Sheaves and Kodaira’s Embedding Theorem

Junjiro Noguchi ()
Additional contact information
Junjiro Noguchi: The University of Tokyo

Chapter Chapter 8 in Analytic Function Theory of Several Variables, 2016, pp 343-366 from Springer

Abstract: Abstract Up to the present we have been dealt with open domains and open complex manifolds. In this chapter we also deal with compact ones. We will introduce a topology in the space of sections of a coherent sheaf. As a consequence we will see that all cohomologies of a coherent sheaf over a compact complex space are finite dimensional (Cartan–Serre Theorem). Furthermore, we will extend Grauert’s Theorem 7.5.26 for a general coherent sheaf. Then, as an application, we prove Kodaira’s Embedding Theorem to embed a Hodge manifold into a complex projective space. Kodaira’s Embedding Theorem provides a bridge between the theory of compact Kähler manifolds and that of complex projective algebraic varieties; it is nice to see such a theorem being naturally proved on the extended line of the theory of coherent sheaves.

Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-0291-5_8

Ordering information: This item can be ordered from
http://www.springer.com/9789811002915

DOI: 10.1007/978-981-10-0291-5_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().