Contents

• Contents
• 1. Preface
• 2. Introduction by pictures
• 3. Some problems in algebraic geometry
• 4. Some global algorithms
  • 1. primary decomposition
  • 2. Normalisation
• 5. Singularities and standard bases
• 6. Some local algorithms
  • 1. Classification of singularities
  • 2. deformations
  • 3. the monodromy
• 7. Computer algebra solutions to singularity problems
  • 1. exactness of the Poincaré complex
  • 2. Zariski's multiplicity conjecture
  • 3. curves with maximal number of singularities
• 8. What else is needed
• Bibliography

* Extended version of invited talk, delivered at the ISSAC'98 conference at Rostock,
13th - 15th August, 1998.