LEADER 03455nam 22005655 450 001 9910370250703321 005 20251113181906.0 010 $a3-030-31163-5 024 7 $a10.1007/978-3-030-31163-6 035 $a(CKB)4940000000158789 035 $a(DE-He213)978-3-030-31163-6 035 $a(MiAaPQ)EBC6005501 035 $a(PPN)242845274 035 $a(MiAaPQ)EBC29079661 035 $a(EXLCZ)994940000000158789 100 $a20200103d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComplex Analytic Cycles I $eBasic Results on Complex Geometry and Foundations for the Study of Cycles /$fby Daniel Barlet, Jón Magnússon 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XI, 533 p. 60 illus.) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v356 311 08$a3-030-31162-7 320 $aIncludes bibliographical references and index. 327 $aPreliminary material -- Multigraphs and Reduced Complex Spaces -- Analysis and Geometry on a Reduced Complex Space -- Families of Cycles in Complex Geometry. 330 $aThe book consists of a presentation from scratch of cycle space methodology in complex geometry. Applications in various contexts are given. A significant portion of the book is devoted to material which is important in the general area of complex analysis. In this regard, a geometric approach is used to obtain fundamental results such as the local parameterization theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle spaces have been used in complex geometry for some forty years. The purpose of the book is to systematically explain these methods in a way which is accessible to graduate students in mathematics as well as to research mathematicians. After the background material which is presented in the initial chapters, families of cycles are treated in the last most important part of the book. Their topological aspects are developed in a systematic way and some basic, important applications of analytic families of cycles are given. The construction ofthe cycle space as a complex space, along with numerous important applications, is given in the second volume. The present book is a translation of the French version that was published in 2014 by the French Mathematical Society. 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x2196-9701 ;$v356 606 $aFunctions of complex variables 606 $aProjective geometry 606 $aSeveral Complex Variables and Analytic Spaces 606 $aProjective Geometry 615 0$aFunctions of complex variables. 615 0$aProjective geometry. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aProjective Geometry. 676 $a516.35 676 $a516.35 700 $aBarlet$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781286 702 $aMagnússon$b Jón$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910370250703321 996 $aComplex Analytic Cycles I$92517210 997 $aUNINA