Abstract | Keywords | Export | Availability | Bookmark

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

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.

Curves, Algebraic. --- Courbes algébriques --- Geometry --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Surfaces, Algebraic --- Degenerations. --- Algebraic curves --- Degenerations of algebraic surfaces --- Mathematics. --- Algebra. --- Algebraic geometry. --- Functions of complex variables. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Algebraic geometry --- Mathematical analysis --- Math --- Science --- Algebraic varieties --- Geometry, algebraic. --- Differential equations, partial. --- Partial differential equations