Splitting Deformations of Degenerations of Complex Curves

Download or read book Splitting Deformations of Degenerations of Complex Curves written by Shigeru Takamura and published by Springer Science & Business Media. This book was released on 2006-07-26 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.