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Splitting Deformations of Degenerations of Complex Curves

Towards the Classification of Atoms of Degenerations, III

  • Shigeru Takamura

Part of the Lecture Notes in Mathematics book series (LNM, volume 1886)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Basic Notions and Ideas

  3. Deformations of Tubular Neighborhoods of Branches

  4. Barking Deformations of Degenerations

  5. Singularities of Subordinate Fibers near Cores

  6. Classification of Atoms of Genus ≤ 5

  7. Back Matter
    Pages 581-594

About this book

Introduction

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.

Keywords

Monodromy Riemann surface Riemann surfaces Singular fiber complex surface deformation of complex structures deformation theory

Editors and affiliations

  • Shigeru Takamura
    • 1
  1. 1.Department of Mathematics Graduate School of ScienceKyoto University606-8502KyotoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-33364-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2006
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-33363-0
  • Online ISBN 978-3-540-33364-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site