Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1886)
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Table of contents (26 chapters)
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Basic Notions and Ideas
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Deformations of Tubular Neighborhoods of Branches
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Barking Deformations of Degenerations
Keywords
About this book
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.
Reviews
From the reviews:
"This is a 590 pages book on deformation theory, using mostly topological methods, but also ‘translated’ to algebraic geometry and using algebraic methods. … It is a nice level and should be possible to read. Most commonly, algebraic geometers translate from differential geometry to solve problems. In this book the concept is vice versa: Algebraic methods are used to solve topological problems. Thus this book may at the first glance look elementary for an algebraist, but it is not." (Arvid Siqveland, Zentralblatt MATH, Vol. 1100 (2), 2007)
Editors and Affiliations
Bibliographic Information
Book Title: Splitting Deformations of Degenerations of Complex Curves
Book Subtitle: Towards the Classification of Atoms of Degenerations, III
Editors: Shigeru Takamura
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-33364-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Softcover ISBN: 978-3-540-33363-0Published: 26 July 2006
eBook ISBN: 978-3-540-33364-7Published: 11 October 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 594
Number of Illustrations: 123 b/w illustrations
Topics: Algebraic Geometry, Several Complex Variables and Analytic Spaces, Algebra