LEADER 03508nam 22005415 450 001 9911011657603321 005 20250624130255.0 010 $a9783031848452 024 7 $a10.1007/978-3-031-84845-2 035 $a(CKB)39449925000041 035 $a(MiAaPQ)EBC32176703 035 $a(Au-PeEL)EBL32176703 035 $a(DE-He213)978-3-031-84845-2 035 $a(OCoLC)1526859229 035 $a(EXLCZ)9939449925000041 100 $a20250624d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComplex Analytic Cycles II $eThe Cycle Space /$fby Daniel Barlet, Jón Magnússon 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (1346 pages) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v363 311 08$a9783031848445 327 $a5 Construction of the Cycle Space -- 6 Relative fundamental classes -- 7 Intersection theory -- 8 Holomorphic currents and Intersection Theory in a nearly smooth complex spaces -- 9 Chow varieties and Cycle spaces -- 10 Douady ?? > Cycles -- 11 Convexity of Cycles space -- 12 Kählerianity of Cycle Spaces. 330 $aThis book is the second volume of a work on complex analytic cycles and the results, stated without proof in the first volume, are proved here. It begins with the construction of the reduced complex space formed by all compact cycles of a given complex space. Following this construction the main subjects of the book are: ? Fundamental class of a cycle and relative fundamental class of an analytic family of cycles ? Intersection theory with parameters on complex manifolds and more generally on nearly smooth complex spaces ? Holomorphic currents on reduced complex spaces ? Chow varieties and cycle spaces of quasi-projective complex spaces ? Natural morphism from the Douady space to the cycle space ? Holomorphic convexity in cycle spaces and integration of $\bar{partial}$-cohomology classes on cycles ? Strong Kählerianity of cycle spaces of Kähler manifolds ? Numerous important applications of cycle space theory Preliminaries needed in the book in addition to the material of the first volume, for instance sheaf cohomology with support, are explained in detail, making this two-volume work quite self-contained. The French version of the present book was published in 2020 by the French Mathematical Society in the series Cours Spécialisés and during the translation process the authors have improved in many ways the original version. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v363 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)$0781286 701 $aMagnússon$b Jón$0781287 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911011657603321 996 $aComplex Analytic Cycles II$94400590 997 $aUNINA