viii CONTENTS Vanishing, singularities and effective bounds via prime characteristic local algebra KAREN E. SMITH 289 III. Motives and Connections with Arithmetic Lectures on mixed motives SPENCER BLOCH 329 Period domains over finite and local fields MICHAEL RAPOPORT 361 Hermitian vector bundles on arithmetic varieties CHRISTOPHE SOULE 383 IV. Real Algebraic Varieties and Singularities Invariants of generic plane curves and invariants of singularities S. M. GUSEIN-ZADE 423 Enumerative geometry for real varieties FRANK SOTTILE 435 Part 2 Preface xi Scientific Program xiii V. Quantum Cohomology and Connections with Physics Seiberg-Witten integrable systems RON DONAGI 3 Notes on stable maps and quantum cohomology W. FULTON AND R. PANDHARIPANDE 45 Mapping class groups and moduli spaces of curves RICHARD HAIN AND EDUARD LOOIJENGA 97 Algebraic and symplectic geometry of Gromov-Witten invariants JUN LI AND GANG TIAN 143
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