Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations

The 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...

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Detalles Bibliográficos
Autor principal: Takamura, Shigeru
Lenguaje:eng
Publicado: Springer 2006
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/978-3-540-33364-7
http://cds.cern.ch/record/1690686
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author Takamura, Shigeru
author_facet Takamura, Shigeru
author_sort Takamura, Shigeru
collection CERN
description The 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.
id cern-1690686
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2006
publisher Springer
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spelling cern-16906862021-04-21T21:14:05Zdoi:10.1007/978-3-540-33364-7http://cds.cern.ch/record/1690686engTakamura, ShigeruSplitting deformations of degenerations of complex curves: towards the classification of atoms of degenerationsMathematical Physics and MathematicsThe 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.Springeroai:cds.cern.ch:16906862006
spellingShingle Mathematical Physics and Mathematics
Takamura, Shigeru
Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title_full Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title_fullStr Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title_full_unstemmed Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title_short Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
title_sort splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-540-33364-7
http://cds.cern.ch/record/1690686
work_keys_str_mv AT takamurashigeru splittingdeformationsofdegenerationsofcomplexcurvestowardstheclassificationofatomsofdegenerations

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