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基本説明
Based on a series of lectures delivered at the Centre de Recherches Mathématiques (CRM). Contents: Complex manifolds, Vector bundles, Kähler manifolds, Line bundles, The Lefschetz (1,1) theorem, and more.
Full Description
This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a 'user-friendly' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry. It includes an appendix by B. Brent Gordon.
Contents
Complex manifolds Vector bundles Kahler manifolds Line bundles The Lefschetz (1,1) theorem The Lefschetz (1,1) theorem revisited Formulation of the general Hodge conjecture Chern class theory Cohomology of complete intersections The Hodge theorem Analytic and topological necessities of the Kahler condition Intermediate Jacobians Various approaches to the Hodge conjecture for varieties with well understood geometric structure The approach to the Hodge conjecture via normal functions Hodge theory and Chow groups Results and formulations in the singular case A survey of the Hodge conjecture for abelian varieties Index Index of notation.
