This book presents some of the proceedings of the conference on Algebraic Geometry held at Sundance, in July 1986, in the mountains near Provo, Utah. Financial support, from the National Science Foundation (grant 86 - 01409) and from Brigham Young University, is gratefully acknowledged. Normally, a proceedings volume collects writups of lecures given at the conference, based on work done earlier, and the present volume, indeed, includes a number of these. We are very pleased, however, that the bulk of this volume presents research begun or carried out right at Sundance. Some of this new work may not have been done at all, had the conference not brought together the individuals involved. Beautiful surroundings, ample and contiguous spaces for lectures and discussions, meals served right beside the working areas: all contributed to an atmosphere unusually conducive to new work. But the major responsibility for the success of the conference lay, we feel, with the participants. Their enthusiasm, their interests, their eagerness, are reflected in the papers which follow. It is a pleasure to thank them here.

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