TY  - BOOK
AU  - Takamura,Shigeru
TI  - Splitting deformations of degenerations of complex curves: towards the classification of atoms of degenerations, iii 
T2  - Lecture notes in mathematics) (V. 3
SN  - 3540333630
U1  - 516 
PY  - 2006///
CY  - [S.l.]
PB  - Springer
KW  - Algebra
KW  - Algebraic Geometry
KW  - Calculus & mathematical analysis
KW  - Mathematics & science
KW  - Mathematics
KW  - Science/Mathematics
KW  - Geometry - Algebraic
KW  - Mathematical analysis
KW  - Mathematics / Geometry / Algebraic
KW  - Mathematics / Mathematical Analysis
KW  - Courbes algâebriques
KW  - Curves, Algebraic
N1  - 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
ER  -