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Algebraic Geometry Santa Cruz 1995
Edited by: János Kollár, University of Utah, Salt Lake City, UT, Robert Lazarsfeld, University of Michigan, Ann Arbor, MI, and David R. Morrison, Duke University, Durham, NC
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Proceedings of Symposia in Pure Mathematics
1997; 896 pp; hardcover
Volume: 62
ISBN-10: 0-8218-0493-6
ISBN-13: 978-0-8218-0493-3
List Price: US$201 Member Price: US$160.80
Order Code: PSPUM/62

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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.

Features:

• Comprehensive coverage of developments over the past decade.
• Emphasis on new directions and future developments.
• Connections to related fields.
• Many expository survey papers.

Graduate students and research mathematicians interested in algebraic geometry and related fields.

Part 1. Geometry and Topology of Algebraic Surfaces
• F. Catanese -- Homological algebra and algebraic surfaces
• C. Ciliberto -- The bicanonical map for surfaces of general type
• R. Friedman -- Donaldson and Seiberg-Witten invariants of algebraic surfaces
• K. G. O'Grady -- Moduli of vector-bundles on surfaces
• M. Teicher -- Braid groups, algebraic surfaces and fundamental groups of complements of branch curves
Higher Dimensional Algebraic Geometry
• M. Andreatta and J. Wiśniewski -- A view on contractions of higher dimensional varieties
• A. Bertram -- Stable pairs and log flips
• L. Ein -- Multiplier ideals, vanishing theorems and applications
• J. Kollár -- Singularities of pairs
• K. E. Smith -- Vanishing, singularities and effective bounds via prime characteristic local algebra
Motives and Connections with Arithmetic
• S. Bloch -- Lectures on mixed motives
• M. Rapoport -- Period domains over finite and local fields
• C. Soulé -- Hermitian vector bundles on arithmetic varieties
Real Algebraic Varieties and Singularities
• S. M. Gusein-Zade -- Invariants of generic plane curves and invariants of singularities
• F. Sottile -- Enumerative geometry for real varieties
Part 2. Quantum Cohomology and Connections with Physics
• R. Donagi -- Seiberg-Witten integrable systems
• W. Fulton and R. Pandharipande -- Notes on stable maps and quantum cohomology
• R. Hain and E. Looijenga -- Mapping class groups and moduli spaces of curves
• J. Li and G. Tian -- Algebraic and symplectic geometry of Gromov-Witten invariants
Fundamental Groups and Non-Abelian Hodge Theory
• L. Katzarkov -- On the Shafarevich maps
• C. Simpson -- The Hodge filtration on nonabelian cohomology
Complex Geometry
• J.-P. Demailly -- Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials
• C. LeBrun -- Twistors for tourists: A pocket guide for algebraic geometers
Toric Geometry
• D. A. Cox -- Recent developments in toric geometry
• B. Sturmfels -- Equations defining toric varieties