Preface The 1995 AMS Summer Research Institute on Algebraic Geometry was held at the University of California, Santa Cruz, from July 9 through July 29, 1995. The organizing committee consisted of Henri Gillet, Janos Kollar, Robert Lazarsfeld (chairman), Robert MacPherson, David Morrison and Yum-Tong Siu. The present volumes contain write-ups of all the plenary lecture series with the exception of E. Witten's course on duality in supersymmetric gauge theories1 and A. J. de Jong's lectures on alterations of singularities2. They also contain a number of survey articles growing out of seminar talks. One of the main thrusts of the Institute was to provide an introduction to some of the exciting new areas and directions that have recently opened up in geometrically oriented algebraic geometry. At the same time, the conference pro- vided a forum for the dissemination of important developments in the more classical branches of the field. A summary of the complete scientific program appears on the following pages. We hope that the papers in these Proceedings will give a sense of the breadth and vitality of algebraic geometry as it emerged at Santa Cruz. How- ever the editors are well aware that, in spite of their best efforts, important areas remain under-represented in these volumes. Finally, on behalf of the whole organizing committee, we would like to thank Chris Harkness and the AMS for their work in the day-to-day organization of the Institute, David Cox and David Perkinson for organizing the graduate student seminar, and the seminar organizers and speakers for their contributions to the scientific program. But we'd particularly like to express our gratitude to all the participants, whose good humor and enthusiasm ensured the success of the Institute. JANOS KOLLAR, ROBERT LAZARSFELD, DAVID R. MORRISON 1 A much expanded version of Witten's lecture series was delivered at the Institute for Ad- vanced Study during 1996-97, and is being written up for publication. 2 de Jong's lectures reported on A. J. de Jong, Smoothness, semi-stability and alterations. Inst. Hautes Etudes Sci. Publ. Math. No. 83 (1996), 51-93. xi
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