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Edited by: Richard Randell

Contemporary Mathematics
1989; 359 pp; softcover
Volume: 90
ISBN-10: 0-8218-5096-2
ISBN-13: 978-0-8218-5096-1
List Price: US$66
Member Price: US$52.80
Order Code: CONM/90
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This volume contains the proceedings of the Institute for Mathematics and its Applications Participating Institutions Conference on Singularities, held at the University of Iowa in July 1986. The conference brought together an international group of researchers in algebraic and analytic singularity theory. This collection consists of research papers related to talks given at the conference.

The field of singularities takes techniques from and gives results to many areas of mathematics, including algebraic and differential geometry and topology, complex analysis, Lie algebras and reflection groups, and combinatorics. All these areas are represented here with an emphasis on local algebraic, analytic and tangential properties, deformation and topology of singularities, and arrangements of hyperplanes.

This volume will be of interest to current and prospective researchers in various aspects of singularity theory, as it provides an overview of the current state of singularity theory and details work in several subareas. Many of the articles provide a basis for further research, and a list of problems presented at the conference is included.

Table of Contents

  • M. Andreatta and A. Sommese -- Generically ample divisors on normal Gorenstein surfaces
  • J. Damon -- Topological equivalence for nonisolated singularities and global affine hypersurfaces
  • M. Falk -- The cohomology and fundamental group of a hyperplane complement
  • T. S. Fukui -- The modified analytic trivialization of a family of real analytic mappings
  • Y.-N. Gau -- On the topological types of quasi-ordinary surface germs
  • H. Hauser and R. Randell -- Report on the problem session
  • S. Ishii -- Two dimensional singularities with bounded pluri-genera \(\delta_m\) are \(Q\)-Gorenstein singularities
  • M. Jambu and H. Terao -- Arrangements of hyperplanes and broken circuits
  • M. Kannowski -- Simply connected four-manifolds obtained from weighted homogeneous polynomials
  • T. Kohno -- Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups
  • H. B. Laufer -- Tangent cones for deformations of two-dimensional quasi-homogeneous singularities
  • M. Oka -- On the weak simultaneous resolution of a negligible truncation of the Newton boundary
  • P. Orlik -- Basic derivations for unitary reflection groups
  • H. Terao and Y. Enta -- Basic derivations for \(G_34\): Appendix to "Basic derivations for unitary reflection groups," by P. Orlik
  • D. B. O'Shea -- Spaces of limiting tangent spaces
  • R. Pellikaan -- Series of isolated singularities
  • D. Siersma -- Quasihomogeneous singularities with transversal type \(A_1\)
  • T. Urabe -- Dynkin graphs and combinations of singularities on plane sextic curves
  • Y.-J. Xu and S. S.-T. Yau -- The inequality \(\mu \ge 12p_g - 4\) for hypersurface weakly elliptic singularities
  • G. M. Ziegler -- Multiarrangements of hyperplanes and their freeness
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