Singularities and Computer Algebra

This volume surveys important topics in singularity theory, with a particular focus on computational aspects of the subject. The contributors to this volume include R. O. Buchweitz, Y. A. Drozd, W. Ebeling, H. A. Hamm, Le D. T., I. Luengo, F.-O. Schreyer, E. Shustin, J. H. M. Steenbrink, D. van Straten, B. Teissier and J. Wahl. Together they describe the development of various areas of singularity theory over many years, and a range of open questions are discussed. Research workers in singularity theory, computer algebra or related subjects will find that this book contains a wealth of valuable information.

Preface; Invited lectures; List of participants; 1. Aspects of Gert-Martin Greuel's mathematical work C. Lossen and G. Pfister; 2. Exterior algebra methods for the construction of rational surfaces in the projective fourspace H. Abo and F.-O. Schreyer; 3. Superisolated surface singularities E. Artal Bartolo, I. Luengo and A. Melle Hernandez; 4. Linear free divisors and quiver representations R.-O. Buchweitz and D. Mond; 5. Derived categories of modules and coherent sheaves Y. A. Drozd; 6. Monodromy W. Ebeling; 7. Algorithmic resolution of singularities A. Fruhbis-Kruger and G. Pfister; 8. Newton polyhedra of descriminants: a computation E. Garci a Barroso and B. Teissier; 9. Depth and differential forms H. A. Hamm; 10. The geometry of the versal deformation L. D. Tráng; 11. 21 years of SINGULAR experiments in mathematics C. Lossen and H. Schonemann; 12. The patchworking construction in tropical enumerative geometry E. Shustin; 13. Adjunction conditions for one-forms on surfaces in projective three-space J. H. M. Steenbrink; 14. Sextic surfaces with ten triple points J. Stevens; 15. Some problems on Lagrangian singularities D. van Straten; 16. Topology, geometry, and equations of normal surface singularities J. Wahl.