Splitting Deformations of Degenerations of Complex Curves: Towards the Classification of Atoms of Degenerations, III. Lecture Notes in Mathematics, Volume 1886.

Author:   Shigeru Takamura
Publisher:   Springer
ISBN:  

9786610635207


Pages:   584
Publication Date:   01 January 2006
Format:   Electronic book text
Availability:   Out of stock   Availability explained
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Splitting Deformations of Degenerations of Complex Curves: Towards the Classification of Atoms of Degenerations, III. Lecture Notes in Mathematics, Volume 1886.


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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 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.

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Author:   Shigeru Takamura
Publisher:   Springer
Imprint:   Springer
ISBN:  

9786610635207


ISBN 10:   661063520
Pages:   584
Publication Date:   01 January 2006
Audience:   General/trade ,  General
Format:   Electronic book text
Publisher's Status:   Active
Availability:   Out of stock   Availability explained
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

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From the reviews: <p> This is a 590 pages book on deformation theory, using mostly topological methods, but also a ~translateda (TM) to algebraic geometry and using algebraic methods. a ] 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)


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