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.
Generically ample divisors on normal Gorenstein surfaces by M. Andreatta and A. Sommese Topological equivalence for nonisolated singularities and global affine hypersurfaces by J. Damon The cohomology and fundamental group of a hyperplane complement by M. Falk The modified analytic trivialization of a family of real analytic mappings by T. S. Fukui On the topological types of quasi-ordinary surface germs by Y.-N. Gau Report on the problem session by H. Hauser and R. Randell Two dimensional singularities with bounded pluri-genera $\delta m$ are $Q$-Gorenstein singularities by S. Ishii Arrangements of hyperplanes and broken circuits by M. Jambu and H. Terao Simply connected four-manifolds obtained from weighted homogeneous polynomials by M. Kannowski Holonomy Lie algebras, logarithmic connections and the lower central series of fundamental groups by T. Kohno Tangent cones for deformations of two-dimensional quasi-homogeneous singularities by H. B. Laufer On the weak simultaneous resolution of a negligible truncation of the Newton boundary by M. Oka Basic derivations for unitary reflection groups by P. Orlik Basic derivations for $G 34$: Appendix to "Basic derivations for unitary reflection groups," by P. Orlik by H. Terao and Y. Enta Spaces of limiting tangent spaces by D. B. O'Shea Series of isolated singularities by R. Pellikaan Quasihomogeneous singularities with transversal type $A 1$ by D. Siersma Dynkin graphs and combinations of singularities on plane sextic curves by T. Urabe The inequality $\mu \ge 12p g - 4$ for hypersurface weakly elliptic singularities by Y.-J. Xu and S. S.-T. Yau Multiarrangements of hyperplanes and their freeness by G. M. Ziegler.