LEADER 03820nam 2200589 450 001 996466663903316 005 20230729144029.0 010 $a1-280-63520-7 010 $a9786610635207 010 $a3-540-33364-9 024 7 $a10.1007/978-3-540-33364-7 035 $a(CKB)1000000000282937 035 $a(SSID)ssj0000249976 035 $a(PQKBManifestationID)11204616 035 $a(PQKBTitleCode)TC0000249976 035 $a(PQKBWorkID)10230914 035 $a(PQKB)10741058 035 $a(DE-He213)978-3-540-33364-7 035 $a(MiAaPQ)EBC4643106 035 $a(MiAaPQ)EBC7202090 035 $a(Au-PeEL)EBL7202090 035 $a(PPN)123133424 035 $a(EXLCZ)991000000000282937 100 $a20230729d2006 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSplitting deformations of degenerations of complex curves $etowards the classification of atoms of degenerations, III /$fShigeru Takamura 205 $a1st ed. 2006. 210 1$aBerlin, Germany :$cSpringer-Verlag,$d[2006] 210 4$dİ2006 215 $a1 online resource (XII, 594 p. 123 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1886 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-33363-0 320 $aIncludes bibliographical references and index. 327 $aBasic Notions and Ideas -- Splitting Deformations of Degenerations -- What is a barking? -- Semi-Local Barking Deformations: Ideas and Examples -- Global Barking Deformations: Ideas and Examples -- Deformations of Tubular Neighborhoods of Branches -- Deformations of Tubular Neighborhoods of Branches (Preparation) -- Construction of Deformations by Tame Subbranches -- Construction of Deformations of type Al -- Construction of Deformations by Wild Subbranches -- Subbranches of Types Al, Bl, Cl -- Construction of Deformations of Type Bl -- Construction of Deformations of Type Cl -- Recursive Construction of Deformations of Type Cl -- Types Al, Bl, and Cl Exhaust all Cases -- Construction of Deformations by Bunches of Subbranches -- Barking Deformations of Degenerations -- Construction of Barking Deformations (Stellar Case) -- Simple Crusts (Stellar Case) -- Compound barking (Stellar Case) -- Deformations of Tubular Neighborhoods of Trunks -- Construction of Barking Deformations (Constellar Case) -- Further Examples -- Singularities of Subordinate Fibers near Cores -- Singularities of Fibers around Cores -- Arrangement Functions and Singularities, I -- Arrangement Functions and Singularities, II -- Supplement -- Classification of Atoms of Genus ? 5 -- Classification Theorem -- List of Weighted Crustal Sets for Singular Fibers of Genus ? 5. 330 $aThe author develops a deformation theory for degenerations of complex curves; specifically, he treats deformations which induce splittings of the singular fiber of a degeneration. He constructs a deformation of the degeneration in such a way that a subdivisor is "barked" (peeled) off from the singular fiber. These "barking deformations" are related to deformations of surface singularities (in particular, cyclic quotient singularities) as well as the mapping class groups of Riemann surfaces (complex curves) via monodromies. Important applications, such as the classification of atomic degenerations, are also explained. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1886 606 $aCurves, Algebraic 615 0$aCurves, Algebraic. 676 $a516.352 700 $aTakamura$b Shigeru$0472497 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466663903316 996 $aSplitting deformations of degenerations of complex curves$9230574 997 $aUNISA