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

ISBN-13: 9783540537373 / Angielski / Miękka / 1991 / 410 str.

David Mond; James Montaldi

Opis

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.

Spis treści

Symmetric lagrangian singularities and Gauss maps of theta divisors.- On infinitesimal deformations of minimally elliptic singularities.- C-Régularité et trivialité topologique.- Folding maps and focal sets.- The dual graph for space curves.- On the components and discriminant of the versal base space of cyclic quotient singularities.- - equivalence and the equivalence of sections of images and discriminants.- Differential forms and hypersurface singularities.- Local reflexional and rotational symmetry in the plane.- The intersection form of a plane isolated line singularity.- On the degree of an equivariant map.- Automorphisms of direct products of algebroid spaces.- Disentanglements.- The euler characteristic of the disentanglement of the image of a corank 1 map germ.- Vanishing cycles for analytic maps.- On complete conditions in enumerative geometry.- Right-symmetry of mappings.- Deformations and the milnor number of non-isolated plane curve singularities.- Vanishing cycles and special fibres.- On the versal deformation of cyclic quotient singularities.- On Canny's roadmap algorithm: orienteering in semialgebraic sets (an application of singularity theory to theoretical robotics).- Elliptic complete intersection singularities.- Pencils of cubic curves and rational elliptic surfaces.

O autorze

James Montaldi is a Reader in Mathematics at the University of Manchester.