This volume contains many of the lectures delivered at the AMS Summer Research Institute on Algebraic Geometry held at the University of California, Santa Cruz in July 1995. The aim of the conference was to provide a comprehensive view of the development of algebraic geometry in the past decade and to lay special emphasis on emerging new directions. The focus of the papers in these volumes is on expository surveys of important areas rather than on technical presentations of new results. These proceedings will be an indispensable reference and guide for researchers in algebraic geometry or nearby fields. It features a comprehensive coverage of developments over the past decade. It has emphasis on new directions and future developments. There are connections to related fields. It includes many expository survey papers.
Part 1. Geometry and Topology of Algebraic Surfaces: Homological algebra and algebraic surfaces by F. Catanese The bicanonical map for surfaces of general type by C. Ciliberto Donaldson and Seiberg-Witten invariants of algebraic surfaces by R. Friedman Moduli of vector-bundles on surfaces by K. G. O'Grady Braid groups, algebraic surfaces and fundamental groups of complements of branch curves by M. Teicher Higher Dimensional Algebraic Geometry: A view on contractions of higher dimensional varieties by M. Andreatta and J. Wisniewski Stable pairs and log flips by A. Bertram Multiplier ideals, vanishing theorems and applications by L. Ein Singularities of pairs by J. Kollar Vanishing, singularities and effective bounds via prime characteristic local algebra by K. E. Smith Motives and Connections with Arithmetic: Lectures on mixed motives by S. Bloch Period domains over finite and local fields by M. Rapoport Hermitian vector bundles on arithmetic varieties by C. Soule Real Algebraic Varieties and Singularities: Invariants of generic plane curves and invariants of singularities by S. M. Gusein-Zade Enumerative geometry for real varieties by F. Sottile Part 2. Quantum Cohomology and Connections with Physics: Seiberg-Witten integrable systems by R. Donagi Notes on stable maps and quantum cohomology by W. Fulton and R. Pandharipande Mapping class groups and moduli spaces of curves by R. Hain and E. Looijenga Algebraic and symplectic geometry of Gromov-Witten invariants by J. Li and G. Tian Fundamental Groups and Non-Abelian Hodge Theory: On the Shafarevich maps by L. Katzarkov The Hodge filtration on nonabelian cohomology by C. Simpson Complex Geometry: Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials by J.-P. Demailly Twistors for tourists: A pocket guide for algebraic geometers by C. LeBrun Toric Geometry: Recent developments in toric geometry by D. A. Cox Equations defining toric varieties by B. Sturmfels.