Abstract
In this chapter the main results of the theory of coherent analytic sheaves for compact blocks Q in ℂm are proved (see Paragraph 3.2). The standard techniques for coherent sheaves and cohomology theory are used, in particular the fact that H q(Q, S) = 0 for large q (see Chapter B.2.5 and 3.4). Moreover we will bring into play the fact that H q(Q, O) = 0 for q ≥ 1. The basic tool which is derived in this chapter is an attaching lemma for analytic sheaf epimorphisms (Theorem 2.3). The proof of this lemma is based on an attaching lemma of H. Cartan for matrices near the identity (Theorem 1.4) and the Runge approximation theorem (Theorem 2.1).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Grauert, H., Remmert, R. (2004). Theorems A and B for Compact Blocks in ℂm . In: Theory of Stein Spaces. Classics in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18921-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-18921-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00373-1
Online ISBN: 978-3-642-18921-0
eBook Packages: Springer Book Archive