Splitting Deformations of Degenerations of Complex Curves
Publication year: 2006
ISBN: 978-3-540-33364-7
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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.
Subject: Mathematics and Statistics, Monodromy, Riemann surface, Riemann surfaces, Singular fiber, complex surface, deformation of complex structures, deformation theory
