Singularity Theory and its Applications: Warwick 1989, Part I: Geometric Aspects of Singularities (Lecture Notes in Mathematics (1462)) (English and French Edition)

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. 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 A workshop on Singularities, Bifuraction 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 original research, stimulated by the symposium and workshop: All have been refereed and none will appear elsewhere. The main topic of volume II is new methods for the study of bifurcations in nonlinear dynamical systems, and applications of these Pt. 1. Geometric Aspects Of Singularities / D. Mond, J. Montaldi (eds.) -- Pt. 2. Singular[i]ties, Bifurcations And Dynamics / M. Roberts, I. Stewart (eds.) Proceedings Of A Year-long Symposium On Singularity Theory And Its Applications, Held At The University Of Warwick In The Academic Year 1988-89. Cf. Pref. Includes Bibliographical References. This volume contains the results of a workshop held at the University of Warwick on singularities, bifurcation and dynamics. It concentrates specifically on connections with algebraic geometry and contains much information on deformation theory, stratifications and applications.