Lecture Notes in Mathematics

Splitting Deformations of Degenerations of Complex Curves

Towards the Classification of Atoms of Degenerations, III

Authors: Takamura, Shigeru

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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)


Table of contents (26 chapters)

Table of contents (26 chapters)
  • Splitting Deformations of Degenerations

    Pages 23-31

  • What is a barking?

    Pages 33-39

  • Semi-Local Barking Deformations: Ideas and Examples

    Pages 41-56

  • Global Barking Deformations: Ideas and Examples

    Pages 57-81

  • Deformations of Tubular Neighborhoods of Branches (Preparation)

    Pages 85-98

Buy this book

eBook $69.99
price for USA in USD
  • ISBN 978-3-540-33364-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA in USD
  • ISBN 978-3-540-33363-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Splitting Deformations of Degenerations of Complex Curves
Book Subtitle
Towards the Classification of Atoms of Degenerations, III
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1886
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-33364-7
DOI
10.1007/978-3-540-33364-7
Softcover ISBN
978-3-540-33363-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 594
Number of Illustrations
123 b/w illustrations
Topics