Splitting Deformations of Degenerations of Complex Curves Towards the Classification of Atoms of Degenerations, III /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Takamura, Shigeru (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1886
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Functions of complex variables.; Algebraic Geometry.; Several Complex Variables and Analytic Spaces.
• Physical Description: XII, 594 p. 123 illus. online resource.
• ISBN: 9783540333647
• ISSN: 0075-8434 ;

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.