Lecture Notes in Mathematics: Towards the Classification of Atoms of Degenerations, III

Takamura, Shigeru

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.

Details

Published by: Springer

Publication Date: 2006-07-26

Format: Paperback

ISBN-13: 9783540333630

DOI: 10.1007/978-3-540-33364-7

Dimensions: 235cm x155cm

Pages: 594