Deformations of Singularities

2003
ISBN: 978-3-540-00560-5
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1811, 166 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 271 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Stevens, Jan

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.