東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Analytic cycles of finite type

Record Type:	Electronic resources : Monograph/item
Title/Author:	Analytic cycles of finite type/ by Daniel Barlet, Jón Ingólfur Magnússon.
Author:	Barlet, D.
other author:	Magnússon, Jón.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xix, 139 p. :ill., digital ;24 cm.
[NT 15003449]:	Chapter 1. Semi-proper maps -- Chapter 2. Quasi-proper Maps -- Chapter 3. The space Cfn (M) -- Chapter 4. f-Analytic Families of Cycles -- Chapter 5. Geometrically f-Flat Maps and Strongly Quasi-proper Maps -- Chapter 6. Applications.
Contained By:	Springer Nature eBook
Subject:	Analytic spaces. -
Online resource:	https://doi.org/10.1007/978-3-031-96406-0
ISBN:	9783031964060

Analytic cycles of finite type
Barlet, D.

Analytic cycles of finite type[electronic resource] /by Daniel Barlet, Jón Ingólfur Magnússon. - Cham :Springer Nature Switzerland :2025. - xix, 139 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23741617-9692 ;. - Lecture notes in mathematics ;v. 2374..

Chapter 1. Semi-proper maps -- Chapter 2. Quasi-proper Maps -- Chapter 3. The space Cfn (M) -- Chapter 4. f-Analytic Families of Cycles -- Chapter 5. Geometrically f-Flat Maps and Strongly Quasi-proper Maps -- Chapter 6. Applications.

This book highlights the use of non-compact analytic cycles in complex geometry. The main focus is on analytic families of cycles of finite type, in other words, cycles which have only finitely many irreducible components. It is shown how the space of all cycles of finite type in a given complex space, endowed with a weak analytic structure, can be used in many ways as the reduced complex space of all compact cycles in the given space. Several illustrative and enlightening examples are provided, as well as applications, giving life to the theory. The exposition includes a characterization of quasi-proper holomorphic maps which admit a geometric flattening, a proof of an existence theorem for meromorphic quotients with respect to a large class of analytic equivalence relations, and a generalization of the Stein factorization to a variety of holomorphic maps. In addition, a study is made of the behavior of analytic families of finite type cycles when they are restricted to Zariski open subsets and extended across analytic subsets. Aimed at researchers and graduate students with an interest in complex or algebraic geometry, the book is adequately self-contained, the basic notions are explained and suitable references are given for auxiliary results that are used in the text.

ISBN: 9783031964060

Standard No.: 10.1007/978-3-031-96406-0doiSubjects--Topical Terms:

579160
Analytic spaces.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Analytic cycles of finite type
LDR:02568nmm a2200337 a 4500 001 2414343
003 DE-He213
005 20250806182247.0
006 m d
007 cr nn 008maaau
008 260205s2025 sz s 0 eng d
020 $a 9783031964060 $q (electronic bk.)
020 $a 9783031964053 $q (paper)
024 7 $a 10.1007/978-3-031-96406-0 $2 doi
035 $a 978-3-031-96406-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.9 $2 23
090 $a QA331 $b .B257 2025
100 1 $a Barlet, D. $3 3789817
245 1 0 $a Analytic cycles of finite type $h [electronic resource] / $c by Daniel Barlet, Jón Ingólfur Magnússon.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2025.
300 $a xix, 139 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2374
505 0 $a Chapter 1. Semi-proper maps -- Chapter 2. Quasi-proper Maps -- Chapter 3. The space Cfn (M) -- Chapter 4. f-Analytic Families of Cycles -- Chapter 5. Geometrically f-Flat Maps and Strongly Quasi-proper Maps -- Chapter 6. Applications.
520 $a This book highlights the use of non-compact analytic cycles in complex geometry. The main focus is on analytic families of cycles of finite type, in other words, cycles which have only finitely many irreducible components. It is shown how the space of all cycles of finite type in a given complex space, endowed with a weak analytic structure, can be used in many ways as the reduced complex space of all compact cycles in the given space. Several illustrative and enlightening examples are provided, as well as applications, giving life to the theory. The exposition includes a characterization of quasi-proper holomorphic maps which admit a geometric flattening, a proof of an existence theorem for meromorphic quotients with respect to a large class of analytic equivalence relations, and a generalization of the Stein factorization to a variety of holomorphic maps. In addition, a study is made of the behavior of analytic families of finite type cycles when they are restricted to Zariski open subsets and extended across analytic subsets. Aimed at researchers and graduate students with an interest in complex or algebraic geometry, the book is adequately self-contained, the basic notions are explained and suitable references are given for auxiliary results that are used in the text.
650 0 $a Analytic spaces. $3 579160
650 0 $a Complex manifolds. $3 660495
650 0 $a Holomorphic mappings. $3 699810
650 0 $a Algebraic cycles. $3 718506
650 1 4 $a Several Complex Variables and Analytic Spaces. $3 893953
650 2 4 $a Projective Geometry. $3 2056109
700 1 $a Magnússon, Jón. $3 3789818
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v v. 2374. $3 3790984
856 4 0 $u https://doi.org/10.1007/978-3-031-96406-0
950 $a Mathematics and Statistics (SpringerNature-11649)