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Analytic cycles of finite type

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analytic cycles of finite typeby Daniel Barlet, Jón Ingólfur Magnússon.
作者:	Barlet, D.
其他作者:	Magnússon, Jón.
出版者:	Cham :Springer Nature Switzerland :2025.
面頁冊數:	xix, 139 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Analytic spaces.
電子資源:	https://doi.org/10.1007/978-3-031-96406-0
ISBN:	9783031964060$q(electronic bk.)

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 ;2035..

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$q(electronic bk.)

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

666703
Analytic spaces.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Analytic cycles of finite type
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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.
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650 2 4 $a Projective Geometry. $3 676333
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