Deformations of singularities
type: Item
instance of: scholarly article
title: Deformations of singularities
zbMATH Open document ID: 1034.14003
author: Jan Stevens
published in: Lecture Notes in Mathematics
publication date: 2003-04-09T00:00:00Z
review text: The lecture notes are based on, respectively influenced by, the Habilitationsschrift of the author. In the first half of the notes, the general deformation theory, especially of deformation of singularities, is developed. It includes standard bases, infinitesimal deformations, deformation of algebras, formal deformation theory, deformation of compact manifolds and the existence of versal deformations for isolated singularities. One can see that many of the problems in deformation theory occur in the (well-established) theories of Kodaira-Spencer (compact complex manifolds) and Thom-Mather (function germs). The remaining chapters of the lecture notes contain more specific problems like quotient singularities, the projection method, Kollár's conjectures (concerning smoothing components of rational surface singularities), and the versal deformation of hyperelliptic cones. Several examples are treated as the versal deformation of the coordinate axes in \(\mathbb{C}^n\), the cone over the rational normal curve of degree four, and 14 lines in general position through the origin in \(\mathbb{C}^6\) (a curve with several smoothing components).
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 14B07
Mathematics Subject Classification ID: 32S30
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 1896086
zbMATH Keywords: singularities
zbMATH Keywords: versal deformation
zbMATH Keywords: infinitesimal deformation
zbMATH Keywords: standard bases
MaRDI profile type: Publication
full work available at URL: b10723
OpenAlex ID: W600946313
DOI: 10.1007/B10723
description: scientific article; zbMATH DE number 1896086