Cycle Spaces of Flag Domains

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139,09 

A Complex Geometric Viewpoint, Progress in Mathematics 245

ISBN: 0817643915
ISBN 13: 9780817643911
Autor: Fels, Gregor/Huckleberry, Alan/Wolf, Joseph A
Verlag: Springer Basel AG
Umfang: xx, 339 S.
Erscheinungsdatum: 12.12.2005
Auflage: 1/2006
Produktform: Gebunden/Hardback
Einband: GEB

This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Key features: * Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist * Many new results presented for the first time * Driven by numerous examples * The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry * Comparisons with classical Barlet cycle spaces are given * Good bibliography and index Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.

Artikelnummer: 1511512 Kategorie:

Beschreibung

Inhaltsangabe* Dedication * Acknowledgments * Introduction Part I: Introduction to Flag Domain Theory Overview * Structure of Complex Flag Manifolds * Real Group Orbits * Orbit Structure for Hermitian Symmetric Spaces * Open Orbits * The Cycle Space of a Flag Domain Part II: Cycle Spaces as Universal Domains Overview * Universal Domains * BInvariant Hypersurfaces in Mz * Orbit Duality via Momentum Geometry * Schubert Slices in the Context of Duality * Analysis of the Boundary of U * Invariant Kobayashi-Hyperbolic Stein Domains * Cycle Spaces of Lower-Dimensional Orbits * Examples Part III: Analytic and Geometric Concequences Overview * The Double Fibration Transform * Variation of Hodge Structure * Cycles in the K3 Period Domain Part IV: The Full Cycle Space Overview * Combinatorics of Normal Bundles of Base Cycles * Methods for Computing H1(C;O(E((q+0q)s))) * Classification for Simple g0 with rank t < rank g * Classification for rank t = rank g * References * Index * Symbol Index

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