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Analytic cycles of finite type

Record Type:	Language materials, printed : 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.;
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 ;1943..

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:

672657
Analytic spaces.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Analytic cycles of finite type
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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 672657
650 0 $a Complex manifolds. $3 676705
650 0 $a Holomorphic mappings. $3 796560
650 0 $a Algebraic cycles. $3 672615
650 1 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Projective Geometry. $3 1021390
700 1 $a Magnússon, Jón. $3 1486980
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