000 03964nam a22004935i 4500
001 978-3-540-33364-7
003 DE-He213
005 20190213151820.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540333647
_9978-3-540-33364-7
024 7 _a10.1007/978-3-540-33364-7
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
245 1 0 _aSplitting Deformations of Degenerations of Complex Curves
_h[electronic resource] :
_bTowards the Classification of Atoms of Degenerations, III /
_cedited by Shigeru Takamura.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXII, 594 p. 123 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1886
505 0 _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.
520 _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.
650 0 _aGeometry, algebraic.
650 0 _aDifferential equations, partial.
650 0 _aAlgebra.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aSeveral Complex Variables and Analytic Spaces.
_0http://scigraph.springernature.com/things/product-market-codes/M12198
650 2 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
700 1 _aTakamura, Shigeru.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540822615
776 0 8 _iPrinted edition:
_z9783540333630
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1886
856 4 0 _uhttps://doi.org/10.1007/978-3-540-33364-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11973
_d11973