Splitting Deformations of Degenerations of Complex Curves Towards the Classification of Atoms of Degenerations, III /

Splitting Deformations of Degenerations of Complex Curves Towards the Classification of Atoms of Degenerations, III /

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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...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Takamura, Shigeru (Editor)
Format: Electronic eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
Series:Lecture Notes in Mathematics, 1886
Subjects:
Mathematics.
Algebra.
Algebraic geometry.
Functions of complex variables.
Algebraic Geometry.
Several Complex Variables and Analytic Spaces.
Online Access:Full Text via HEAL-Link
Table of Contents:
  • Basic Notions and Ideas
  • Splitting Deformations of Degenerations
  • What is a barking?
  • Semi-Local Barking Deformations: Ideas and Examples
  • Global Barking Deformations: Ideas and Examples
  • Deformations of Tubular Neighborhoods of Branches
  • Deformations of Tubular Neighborhoods of Branches (Preparation)
  • Construction of Deformations by Tame Subbranches
  • Construction of Deformations of type Al
  • Construction of Deformations by Wild Subbranches
  • Subbranches of Types Al, Bl, Cl
  • Construction of Deformations of Type Bl
  • Construction of Deformations of Type Cl
  • Recursive Construction of Deformations of Type Cl
  • Types Al, Bl, and Cl Exhaust all Cases
  • Construction of Deformations by Bunches of Subbranches
  • Barking Deformations of Degenerations
  • Construction of Barking Deformations (Stellar Case)
  • Simple Crusts (Stellar Case)
  • Compound barking (Stellar Case)
  • Deformations of Tubular Neighborhoods of Trunks
  • Construction of Barking Deformations (Constellar Case)
  • Further Examples
  • Singularities of Subordinate Fibers near Cores
  • Singularities of Fibers around Cores
  • Arrangement Functions and Singularities, I
  • Arrangement Functions and Singularities, II
  • Supplement
  • Classification of Atoms of Genus ? 5
  • Classification Theorem
  • List of Weighted Crustal Sets for Singular Fibers of Genus ? 5.

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