Singularities and Computer Algebra

doi:10.1017/CBO9780511526374

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.

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Singularities and Computer Algebra

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Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

Invited Lectures
pp xiii-xiv

List of Participants
pp xv-xvi

Aspects of Gert-Martin Greuel's Mathematical Work
pp xvii-xxxvi

Exterior Algebra Methods for the Construction of Rational Surfaces in the Projective Fourspace
pp 1-12

Superisolated Surface Singularities
pp 13-40

Linear Free Divisors and Quiver Representations
pp 41-78

Derived Categories of Modules and Coherent Sheaves
pp 79-128

Monodromy
pp 129-156

Algorithmic Resolution of Singularities
pp 157-184

Newton Polyhedra of Discriminants: A Computation
pp 185-210

Depth and Differential Forms
pp 211-232

The Geometry of the Versal Deformation
pp 233-246

21 Years of SINGULAR Experiments in Mathematics
pp 247-272

The Patchworking Construction in Tropical Enumerative Geometry
pp 273-300

Adjunction Conditions for One-Forms on Surfaces in Projective Three-Space
pp 301-314

Sextic Surfaces with Ten Triple Points
pp 315-332

Sextic Surfaces with 10 Triple Points
pp 333-350

Topology, Geometry, and Equations of Normal Surface Singularities
pp 351-372

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