Splitting Deformations of Degenerations of Complex Curves: Towards the Classification of Atoms of Degenerations, III (Lecture Notes in Mathematics)

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9783540333630: Splitting Deformations of Degenerations of Complex Curves: Towards the Classification of Atoms of Degenerations, III (Lecture Notes in Mathematics)

Here is a deformation theory for degenerations of complex curves; specifically, discussing deformations which induce splitting of the singular fiber of a degeneration. The author constructs a deformation of the degeneration in such a way that a subdivisor is "barked," or peeled off from the singular fiber. "Barking deformations" are related to deformations of surface singularities, in particular, cyclic quotient singularities, as well as the mapping class groups of Riemann surfaces via monodromies.

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"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)

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