Singularity Theory and its Applications: Warwick 1989, Part I: Geometric Aspects of Singularities

Malcolm R. Adams, Clint McCrory (auth.), David Mond, James Montaldi (eds.)9780387537375, 0387537376

A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications. The proceedings fall into two halves: Volume I mainly on connections with algebraic geometry and volume II on connections with dynamical systems theory, bifurcation theory, and applications in the sciences. The papers are orginal research, stimulated by the symposium and workshops: All have been refereed, and none will appear elsewhere. The main topic, deformation theory, is represented by several papers on descriptions of the bases of versal deformations, and several more on descriptions of the generic fibres. Other topics include stratifications, and applications to differential geometry.

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Table of contents :
Symmetric lagrangian singularities and Gauss maps of theta divisors….Pages 1-26
On infinitesimal deformations of minimally elliptic singularities….Pages 27-41
C-Régularité et trivialité topologique….Pages 42-62
Folding maps and focal sets….Pages 63-72
The dual graph for space curves….Pages 73-80
On the components and discriminant of the versal base space of cyclic quotient singularities….Pages 81-92
– equivalence and the equivalence of sections of images and discriminants….Pages 93-121
Differential forms and hypersurface singularities….Pages 122-153
Local reflexional and rotational symmetry in the plane….Pages 154-171
The intersection form of a plane isolated line singularity….Pages 172-184
On the degree of an equivariant map….Pages 185-193
Automorphisms of direct products of algebroid spaces….Pages 194-198
Disentanglements….Pages 199-211
The euler characteristic of the disentanglement of the image of a corank 1 map germ….Pages 212-220
Vanishing cycles for analytic maps….Pages 221-234
On complete conditions in enumerative geometry….Pages 235-257
Right-symmetry of mappings….Pages 258-275
Deformations and the milnor number of non-isolated plane curve singularities….Pages 276-291
Vanishing cycles and special fibres….Pages 292-301
On the versal deformation of cyclic quotient singularities….Pages 302-319
On Canny’s roadmap algorithm: orienteering in semialgebraic sets (an application of singularity theory to theoretical robotics)….Pages 320-339
Elliptic complete intersection singularities….Pages 340-372
Pencils of cubic curves and rational elliptic surfaces….Pages 373-405