000			02982nam 2200301| 4500
001			84726
005			20211203170934.0
010			_a978-981-10-0291-5 _dcompra
090			_a84726
100			_a20190128d2016 k||y0pory50 ba
101			_aeng
102			_aSG
200			_aAnalytic function theory of several variables _bDocumento eletrónico _eelements of Oka’s coherence _fJunjiro Noguchi
210			_aSingapore _cSpringer _d2016
215			_aXVIII, 397 p. _cil.
300			_aColocação: Online
303			_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			_aEquações diferenciais parciais
606			_aÁlgebra
606			_aGeometria algébrica
680			_aQA331
700			_aNoguchi _bJunjiro
801			_gRPC _aPT
856			_uhttps://doi.org/10.1007/978-981-10-0291-5
942			_2lcc _cF _n0