Lecture Notes in Mathematics : Lecture Notes in Mathematics - Jan Stevens

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Lecture Notes in Mathematics

By: Jan Stevens

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Paperback | 27 February 2003

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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.

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Non-Fiction Mathematics Geometry Algebraic Geometry Calculus & Mathematical Analysis Differential & Riemannian Geometry Probability & Statistics

Introduction	p. 1
Deformations of singularities	p. 5
Standard bases	p. 15
Infinitesimal deformations	p. 23
Example: the fat point of multiplicity four	p. 33
Deformations of algebras	p. 39
Formal deformation theory	p. 45
Deformations of compact manifolds	p. 55
How to solve the deformation equation	p. 63
Convergence for isolated singularities	p. 67
Quotient singularities	p. 71
The projection method	p. 79
Formats	p. 93
Smoothing components of curves	p. 105
Kollar's conjectures	p. 113
Cones over curves	p. 125
The versal deformation of hyperelliptic cones	p. 137
References	p. 147
Index	p. 155
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Mathematics

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