Author	Stevens, Jan. author
Title	Deformations of Singularities [electronic resource] / by Jan Stevens
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect to	http://dx.doi.org/10.1007/b10723
Descript	X, 166 p. online resource

These notes deal with deformation theory of complex analytic singularities and related objects. The first part treats general theory. The central notion is that of versal deformation in several variants. The theory is developed both in an abstract way and in a concrete way suitable for computations. The second part deals with more specific problems, specially on curves and surfaces. Smoothings of singularities are the main concern. Examples are spread throughout the text

Introduction -- Deformations of singularities -- Standard bases -- Infinitesimal deformations -- Example: the fat point of multiplicity four -- Deformations of algebras -- Formal deformation theory -- Deformations of compact manifolds -- How to solve the deformation equation -- Convergence for isolated singularities -- Quotient singularities -- The projection method -- Formats -- Smoothing components of curves -- Kollรกr's conjectures -- Cones over curves -- The versal deformation of hyperelliptic cones -- References -- Index

1. Mathematics
2. Algebraic geometry
3. Functions of complex variables
4. Differential geometry
5. Mathematics
6. Differential Geometry
7. Several Complex Variables and Analytic Spaces
8. Algebraic Geometry