Deformations of Singularities

• Main Author: Stevens, Jan (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1811
• Subjects: Differential geometry.; Functions of complex variables.; Algebraic geometry.; Differential Geometry.; Several Complex Variables and Analytic Spaces.; Algebraic Geometry.

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....

Table of Contents:

• 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
• Kollár's conjectures
• Cones over curves
• The versal deformation of hyperelliptic cones
• References
• Index.