Singularity Theory
Proceedings of the European Singularities Conference, August 1996, Liverpool and Dedicated to C.T.C. Wall on the Occasion of his 60th Birthday

An up-to-date survey of research in singularity theory.

W. Bruce (Edited by), D. Mond (Edited by)

9780521658881, Cambridge University Press

Paperback, published 3 June 1999

468 pages, 50 b/w illus. 35 tables
22.9 x 15.3 x 2.5 cm, 0.68 kg

' … presents an up-to-date survey of research in this area.' Extrait de L'Enseignement Mathématique

Singularity theory is a broad subject with vague boundaries. It draws on many other areas of mathematics, and in turn has contributed to many areas both within and outside mathematics, in particular differential and algebraic geometry, knot theory, differential equations, bifurcation theory, Hamiltonian mechanics, optics, robotics and computer vision. This volume consists of two dozen articles from some of the best known figures in singularity theory, and it presents an up-to-date survey of research in this area.

Part I. Complex Singularities: 1. Singularities arising from lattice polytopes K. Altmann
2. Critical points of affine multiforms on the complement of arrangements J. N. Damon
3. Strange duality, mirror symmetry and the Leech lattice W. Ebeling
4. Geometry of equisingular families of curves G.-M. Greuel and E. Shustin
5. Arrangements, KZ systems and Lie algebra homology E. J. N. Looijenga
6. The signature of f(x,y) +zN A. Nemethi
7. Spectra of K-unimodal isolated singularities of complete intersections J. M. Steenbrink
8. Dynkin graphs, Gabrielov graphs and triangle singularities T. Urabe
Part II. Stratifications and Equisingularity Theory: 9. Differential forms on singular varieties and cyclic homology J. P. Brasselet and Y. Legrand
10. Continuous controlled vector fields A. A. du Plessis
11. Finiteness of Mather's canonical stratification A. A. du Plessis
12. Trends in equisingularity theory T. J. Gaffney and D. Massey
13. Regularity at infinity of real and complex polynomial maps M. Tibar
Part III. Global Singularity Theory: 14. A Bennequin number estimate for transverse knots V. V. Goryunov and J. W. Hill
15. Abelian covers of the projective plane A. Libgober
16. Elimination of singularities: Thom polynomials and beyond O. Saeki and K. Sukuma
Part IV. Singularities of Mappings: 17. An introduction to the image-computing spectral sequence K. A. Houston
18. On the classification and geometry of Corank 1 map-germs from 3-space to 4-space K. A. Houston and N. P. Kirk
19. Multiplicities of zero-schemes in quasi-homogeneous Corank-1 singularities W. L. Marar, J. A. Montaldi and M. A. S. Ruas
20. Butterflies and umbilics of stable perturbations of analytic map-germs C5,0 ? C4,0 T. Fukui
Part V. Applications of Singularity Theory: 21. Singular phenomena in kinematics P. S. Donelan and C. G. Gibson
22. Singularities of developable surfaces G. Ishikawa
23. Singularities of solutions for first order partial differential equations S. Izumiya.

Subject Areas: Algebraic geometry [PBMW]