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  • © 2003

Deformations of Singularities

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1811)

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Table of contents (19 chapters)

  1. Front Matter

    Pages N2-VII
  2. Introduction

    • Jan Stevens
    Pages 1-4
  3. 1. Deformations of singularities

    • Jan Stevens
    Pages 5-14
  4. 2. Standard bases

    • Jan Stevens
    Pages 15-22
  5. 3. Infinitesimal deformations

    • Jan Stevens
    Pages 23-31
  6. 5. Deformations of algebras

    • Jan Stevens
    Pages 39-44
  7. 6. Formal deformation theory

    • Jan Stevens
    Pages 45-53
  8. 7. Deformations of compact manifolds

    • Jan Stevens
    Pages 55-61
  9. 10. Quotient singularities

    • Jan Stevens
    Pages 71-77
  10. 11. The projection method

    • Jan Stevens
    Pages 79-92
  11. 12. Formats

    • Jan Stevens
    Pages 93-104
  12. 13. Smoothing components of curves

    • Jan Stevens
    Pages 105-111
  13. 14. Kollár’s conjectures

    • Jan Stevens
    Pages 113-124
  14. 15. Cones over curves

    • Jan Stevens
    Pages 125-136
  15. References

    • Jan Stevens
    Pages 147-153
  16. Index

    • Jan Stevens
    Pages 155-157

About this book

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.

Keywords

  • Singularity
  • deformation
  • deformation theory
  • manifold
  • quasi-cone
  • smoothing
  • versality

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions