LEADER 04365nam 22005775 450 001 9910254094803321 005 20230828191654.0 010 $a981-10-0291-6 024 7 $a10.1007/978-981-10-0291-5 035 $a(CKB)3710000000837591 035 $a(DE-He213)978-981-10-0291-5 035 $a(MiAaPQ)EBC6315292 035 $a(MiAaPQ)EBC5555628 035 $a(Au-PeEL)EBL5555628 035 $a(OCoLC)1059412385 035 $a(PPN)194802493 035 $a(EXLCZ)993710000000837591 100 $a20160816d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalytic Function Theory of Several Variables $eElements of Oka?s Coherence /$fby Junjiro Noguchi 205 $a1st ed. 2016. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2016. 215 $a1 online resource (XVIII, 397 p. 28 illus., 27 illus. in color.) 311 $a981-10-0289-4 327 $aHolomorphic Functions -- Oka's First Coherence Theorem -- Sheaf Cohomology -- Holomorphically Convex Domains and Oka--Cartan's Fundamental Theorem -- Domains of Holomorphy -- Analytic Sets and Complex Spaces -- Pseudoconvex Domains and Oka's Theorem -- Cohomology of Coherent Sheaves and Kodaira's Embedding Theorem -- On Coherence -- Appendix -- References -- Index -- Symbols. 330 $aThe purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert?Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps). The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later. The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka?Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan?Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of "Coherence". It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students. 606 $aFunctions of complex variables 606 $aAlgebra, Homological 606 $aGeometry, Algebraic 606 $aSeveral Complex Variables and Analytic Spaces 606 $aCategory Theory, Homological Algebra 606 $aAlgebraic Geometry 615 0$aFunctions of complex variables. 615 0$aAlgebra, Homological. 615 0$aGeometry, Algebraic. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aCategory Theory, Homological Algebra. 615 24$aAlgebraic Geometry. 676 $a515.94 700 $aNoguchi$b Junjiro$4aut$4http://id.loc.gov/vocabulary/relators/aut$059671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254094803321 996 $aAnalytic function theory of several variables$91523146 997 $aUNINA