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Singularities Proceedings of the IMA Participating Institutions Conference Held July 28-August 1, 1986 Singularities Proceedings of the IMA Participating Institutions Conference held July 28-August 1, 1986 AMERICAn MATHEMATICAL SOCIETY UOLUME BO http://dx.doi.org/10.1090/conm/090 Titles in This Series Volume 1 Markov random fields and their 19 Proceedings of th~ Northwestern applications, Ross Kindermann and homotopy theory conference, Haynes J. Laurie Snell R. Miller and Stewart B. Priddy, Editors 2 Proceedings of the conference on 20 Low dimensional topology, Samuel J. integration, topology, and geometry in Lomonaco, Jr., Editor linear spaces, William H. Graves, Editor 21 Topological methods in nonlinear 3 The closed graph and P-closed functional analysis, S. P. Singh, graph properties in general topology, S. Thomaier, and B. Watson, Editors T. R. Hamlett and L. L. Herrington 22 Factorizations of b" ± 1, b = 4 Problems of elastic stability and 2, 3, 5, 6, 7, 10, vibrations, Vadim Komkov, Editor 11, 12 up to high powers, John Brillhart, 5 Rational constructions of modules D. H. Lehmer, J. L. Selfridge, Bryant for simple Lie algebras, George B. Tuckerman, and S. S. Wagstaff, Jr. Seligman 23 Chapter 9 of Ramanujan's second 6 Umbral calculus and Hopf algebras, notebook-Infinite series identities, Robert Morris, Editor transformations, and evaluations, Bruce C. Berndt and Padmini T. Joshi 7 Complex contour integral representation of cardinal spline 24 Central extensions, Galois groups, and functions, Walter Schempp ideal class groups of number fields, A. Frohlich 8 Ordered fields and real algebraic geometry, D. W. Dubois and T. Recio, 25 Value distribution theory and its Editors applications, Chung-Chun Yang, Editor 9 Papers in algebra, analysis and 26 Conference in modern analysis statistics, R. Lidl, Editor and probability, Richard Beals, 10 Operator algebras and K-theory, Anatole Beck, Alexandra Bellow, and Ronald G. Douglas and Claude Arshag Hajian, Editors Schochet, Editors 27 Microlocal analysis, M. Salah Baouendi, 11 Plane ellipticity and related problems, Richard Beals, and Linda Preiss Robert P. Gilbert, Editor Rothschild, Editors 12 Symposium on algebraic topology in 28 Fluids and plasmas: geometry and honor of Jose Adem, Samuel Gitler, dynamics, Jerrold E. Marsden, Editor Editor 29 Automated theorem proving, W. W. 13 Algebraists' homage: Papers in Bledsoe and Donald Loveland, Editors ring theory and related topics, 30 Mathematical applications of category S. A. Amitsur, D. J. Saltman, and theory, J. W. Gray, Editor G. B. Seligman, Editors 31 Axiomatic set theory, James E. 14 Lectures on Nielsen fixed point theory, Baumgartner, Donald A. Martin, and Boju Jiang Saharon Shelah, Editors 15 Advanced analytic number theory. 32 Proceedings of the conference on Part 1: Ramification theoretic methods, Banach algebras and several complex Carlos J. Moreno variables, F. Greenleaf and D. Gulick, 16 Complex representations of GL(2, K) for Editors finite fields K, llya Piatetski-Shapiro 33 Contributions to group theory, 17 Nonlinear partial differential equations, Kenneth I. Appel, John G. Ratcliffe, and Joel A. Smeller, Editor Paul E. Schupp, Editors 18 Fixed points and nonexpansive 34 Combinatorics and algebra, Curtis mappings, Robert C. Sine, Editor Greene, Editor Titles in This Series Volume 35 Four-manifold theory, Cameron Gordon 53 The Selberg trace formula and related and Robion Kirby, Editors topics, Dennis A. Hejhal, Peter Sarnak, 36 Group actions on manifolds, Reinhard and Audrey Anne Terras, Editors Schultz, Editor 54 Differential analysis and infinite 37 Conference on algebraic topology in dimensional spaces, Kondagunta honor of Peter Hilton, Renzo Piccinini Sundaresan and Srinivasa Swaminathan, and Denis Sjerve, Editors Editors 38 Topics in complex analysis, Dorothy 55 Applications of algebraic K-theory to Browne Shaffer, Editor algebraic geometry and number theory, Spencer J. Bloch, R. Keith Dennis, Eric 39 Errett Bishop: Reflections on him and M. Friedlander, and Michael R. Stein, his research, Murray Rosenblatt, Editor Editors 40 Integral bases for affine Lie algebras 56 Multiparameter bifurcation theory, and their universal enveloping algebras, Martin Golubitsky and David Mitzman John Guckenheimer, Editors 41 Particle systems, random media and 57 Combinatorics and ordered sets, large deviations, Richard Durrett, Editor Ivan Rival, Editor 42 Classical real analysis, Daniel 58.1 The Lefschetz centennial conference. Waterman, Editor Part 1: Proceedings on algebraic 43 Group actions on rings, Susan geometry, D. Sundararaman, Editor Montgomery, Editor 58.11 The Lefschetz centennial conference. 44 Combinatorial methods in topology and Part II: Proceedings on algebraic algebraic geometry, John R. Harper topology, S. Gitler, Editor and Richard Mandelbaum, Editors 58.111 The Lefschetz centennial conference. 45 Finite groups-coming of age, John Part Ill: Proceedings on differential McKay, Editor equations, A. Verjovsky, Editor 46 Structure of the standard modules 59 Function estimates, J. S. Marron, Editor for the affine Lie algebra A (1 ) 1 ' 60 Nonstrictly hyperbolic conservation James Lepowsky and Mirko Prime laws, Barbara Lee Keyfitz and 47 Linear algebra and its role in Herbert C. Kranzer, Editors systems theory, Richard A. Brualdi, 61 Residues and traces of differential David H. Carlson, Biswa Nath Datta forms via Hochschild homology, Charles R. Johnson, and Robert J. ' Joseph Lipman Plemmons, Editors 62 Operator algebras and mathematical 48 Analytic functions of one complex physics, Palle E. T. Jorgensen and variable, Chung-chun Yang and Paul S. Muhly, Editors Chi-tai Chuang, Editors 63 Integral geometry, Robert L. Bryant, 49 Complex differential geometry and Victor Guillemin, Sigurdur Helgason, and nonlinear differential equations, R. 0. Wells, Jr., Editors Yum-Tong Siu, Editor 64 The legacy of Sonya Kovalevskaya, 50 Random matrices and their Linda Keen, Editor applications, Joel E. Cohen, Harry Kesten, and Charles M. Newman, 65 Logic and combinatorics, Stephen G. Editors Simpson, Editor 51 Nonlinear problems in geometry, 66 Free group rings, Narian Gupta Dennis M. DeTurck, Editor 67 Current trends in arithmetical algebraic 52 Geometry of normed linear spaces, geometry, Kenneth A. Ribet, Editor R. G. Bartle, N. T. Peck, A. L. Peressini, 68 Differential geometry: The interface and J. J. Uhl, Editors between pure and applied mathematics, Titles in This Series Volume Mladen Luksic, Clyde Martin, and 80 Statistical inference from stochastic William Shadwick, Editors processes, N. U. Prabhu, Editor 69 Methods and applications of 81 Hamiltonian dynamical systems, mathematical logic, Walter A. Carnielli Kenneth R. Meyer and Donald G. Saari, and Luiz Paulo de Alcantara, Editors Editors 70 Index theory of elliptic operators, 82 Classical groups and related topics, foliations, and operator algebras, Alexander J. Hahn, Donald G. James, Jerome Kaminker, Kenneth C. Millett, and Zhe-xian Wan, Editors and Claude Schochet, Editors 83 Algebraic K-theory and algebraic 71 Mathematics and general relativity, number theory, Michael R. Stein and James A. Isenberg, Editor R. Keith Dennis, Editors 72 Fixed point theory and its applications, 84 Partition problems in topology, R. F. Brown, Editor Stevo Todorcevic 73 Geometry of random motion, Rick 85 Banach space theory, Bor-Luh Lin, Durrett and Mark A. Pinsky, Editors Editor 74 Geometry of group representations, 86 Representation theory and number William M. Goldman a11d Andy R. Magid, theory in connection with the local Editors Langlands conjecture, J. Ritter, Editor 75 The finite calculus associated with 87 Abelian group theory, Laszlo Fuchs, Bessel functions, Frank M. Cholewinski Rudiger Gobel, and Phillip Schultz, 76 The structure of finite algebras, Editors David C. Hobby and Ralph Mckenzie 88 Invariant theory, R. Fossum, 77 Number theory and its applications in W. Haboush, M. Hochster, and China, Wang Yuan, Yang Chung-chun, V. Lakshmibai, Editors and Pan Chengbiao, Editors 89 Graphs and algorithms, R. Bruce 78 Braids, Joan S. Birman and Anatoly Richter, Editor Libgober, Editors 90 Singularities, Richard Randell, Editor 79 Regular differential forms, Ernst Kunz and Rolf Waldi Singularities I Volume90 Singularities Proceedings of the IMA Participating Institutions Conference held July 28-August 1 1 19861 with support from the Participating Institutions of the Institute for Mathematics and its Applications and the University of Iowa Richard Randell, Editor AMERICAn MATHEMATICAL SOCIETY Providence • RhOde Island EDITORIAL BOARD Daniel M. Burns, Jr., managing editor Richard W. Beals Sylvain Cappel! David Eisenbud Gerald J. Janusz Jonathan Goodman Jan Mycielski Michael E. Taylor The IMA Participating Institutions Conference on Singularities was held July 28-August 1, 1986 with support from the Participating Institutions of the Institute for Mathematics and Its Applications and the University of Iowa. 1980 Mathematics Subject Classification (1985 Revision). Primary 14B05, 32B30, 32C40, 57R45. Library of Congress Cataloging-in-Publication Data IMA Participating Institutions Conference (1986: University of Iowa) Singularities; proceedings of the IMA Participating Institutions Conference held July 28-August 1, 1986, with support from the participating institutions of the Institute for Mathematics and Its Applications and the University of Iowa. (Contemporary mathematics, ISSN 0271-4132; v. 90) Bibliography: p. ISBN 0-8218-5096-2 ( alk. paper) 1. Singularities (Mathematics)-Congresses. I. Randell, Richard. II. Institute for Mathematics and Its Applications. Ill. University of Iowa. IV. Title.
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