LEADER 03368nam 22005535 450 001 9911018755303321 005 20251208184637.0 010 $a3-031-96406-3 024 7 $a10.1007/978-3-031-96406-0 035 $a(CKB)40161562200041 035 $a(DE-He213)978-3-031-96406-0 035 $a(MiAaPQ)EBC32256154 035 $a(Au-PeEL)EBL32256154 035 $a(OCoLC)1535966561 035 $a(PPN)289108527 035 $a(EXLCZ)9940161562200041 100 $a20250806d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnalytic Cycles of Finite Type /$fby Daniel Barlet, Jón Ingólfur Magnússon 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (XIX, 139 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2374 311 08$a3-031-96405-5 327 $aChapter 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. 330 $aThis book highlights the use of non-compact analytic cycles in complex geometry. The main focus is on analytic families of cycles of finite type, in other words, cycles which have only finitely many irreducible components. It is shown how the space of all cycles of finite type in a given complex space, endowed with a weak analytic structure, can be used in many ways as the reduced complex space of all compact cycles in the given space. Several illustrative and enlightening examples are provided, as well as applications, giving life to the theory. The exposition includes a characterization of quasi-proper holomorphic maps which admit a geometric flattening, a proof of an existence theorem for meromorphic quotients with respect to a large class of analytic equivalence relations, and a generalization of the Stein factorization to a variety of holomorphic maps. In addition, a study is made of the behavior of analytic families of finite type cycles when they are restricted to Zariski open subsets and extended across analytic subsets. Aimed at researchers and graduate students with an interest in complex or algebraic geometry, the book is adequately self-contained, the basic notions are explained and suitable references are given for auxiliary results that are used in the text. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2374 606 $aFunctions of complex variables 606 $aGeometry, Projective 606 $aSeveral Complex Variables and Analytic Spaces 606 $aProjective Geometry 615 0$aFunctions of complex variables. 615 0$aGeometry, Projective. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aProjective Geometry. 676 $a515.94 700 $aBarlet$b D$g(Daniel),$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781286 702 $aMagnu?sson$b Jo?n$g(Jo?n Ingo?lfur),$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911018755303321 996 $aAnalytic Cycles of Finite Type$94431932 997 $aUNINA