國立虎尾科技大學 |

Analytic Function Theory of Several Variables = Elements of Oka’s Coherence /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Analytic Function Theory of Several Variables/ by Junjiro Noguchi.
其他題名:	Elements of Oka’s Coherence /
作者:	Noguchi, Junjiro.
面頁冊數:	XVIII, 397 p. 28 illus., 27 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Functions of complex variables. -
電子資源:	https://doi.org/10.1007/978-981-10-0291-5
ISBN:	9789811002915

Analytic Function Theory of Several Variables = Elements of Oka’s Coherence /
Noguchi, Junjiro.

Analytic Function Theory of Several VariablesElements of Oka’s Coherence /[electronic resource] :by Junjiro Noguchi. - 1st ed. 2016. - XVIII, 397 p. 28 illus., 27 illus. in color.online resource.

Holomorphic 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.

The 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.

ISBN: 9789811002915

Standard No.: 10.1007/978-981-10-0291-5doiSubjects--Topical Terms:

528649
Functions of complex variables.

LC Class. No.: QA331.7

Dewey Class. No.: 515.94

Analytic Function Theory of Several Variables = Elements of Oka’s Coherence /
LDR:03854nam a22003975i 4500 001 981563
003 DE-He213
005 20200701175128.0
007 cr nn 008mamaa
008 201211s2016 si | s |||| 0|eng d
020 $a 9789811002915 $9 978-981-10-0291-5
024 7 $a 10.1007/978-981-10-0291-5 $2 doi
035 $a 978-981-10-0291-5
050 4 $a QA331.7
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.94 $2 23
100 1 $a Noguchi, Junjiro. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1023279
245 1 0 $a Analytic Function Theory of Several Variables $h [electronic resource] : $b Elements of Oka’s Coherence / $c by Junjiro Noguchi.
250 $a 1st ed. 2016.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a XVIII, 397 p. 28 illus., 27 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Holomorphic 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.
520 $a The 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.
650 0 $a Functions of complex variables. $3 528649
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 0 $a Algebraic geometry. $3 1255324
650 1 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a Algebraic Geometry. $3 670184
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811002892
776 0 8 $i Printed edition: $z 9789811002908
776 0 8 $i Printed edition: $z 9789811091247
856 4 0 $u https://doi.org/10.1007/978-981-10-0291-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)