Cycle Spaces of Flag Domains [electronic resource] : A Complex Geometric Viewpoint / by Gregor Fels, Alan Huckleberry, Joseph A. Wolf.

By: Fels, Gregor [author.]
Contributor(s): Huckleberry, Alan [author.] | Wolf, Joseph A [author.] | SpringerLink (Online service)
Material type: TextTextSeries: Progress in Mathematics: 245Publisher: Boston, MA : Birkhäuser Boston, 2006Description: XX, 339 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780817644796Subject(s): Mathematics | Algebraic geometry | Topological groups | Lie groups | Global analysis (Mathematics) | Manifolds (Mathematics) | Functions of complex variables | Differential geometry | Quantum physics | Mathematics | Differential Geometry | Topological Groups, Lie Groups | Several Complex Variables and Analytic Spaces | Global Analysis and Analysis on Manifolds | Algebraic Geometry | Quantum PhysicsAdditional physical formats: Printed edition:: No titleDDC classification: 516.36 LOC classification: QA641-670Online resources: Click here to access online
Contents:
to Flag Domain Theory -- Structure of Complex Flag Manifolds -- Real Group Orbits -- Orbit Structure for Hermitian Symmetric Spaces -- Open Orbits -- The Cycle Space of a Flag Domain -- Cycle Spaces as Universal Domains -- Universal Domains -- B-Invariant 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 -- Analytic and Geometric Consequences -- The Double Fibration Transform -- Variation of Hodge Structure -- Cycles in the K3 Period Domain -- The Full Cycle Space -- Combinatorics of Normal Bundles of Base Cycles -- Methods for Computing H1(C; O) -- Classification for Simple with rank < rank -- Classification for rank = rank .
In: Springer eBooksSummary: 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.
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to Flag Domain Theory -- Structure of Complex Flag Manifolds -- Real Group Orbits -- Orbit Structure for Hermitian Symmetric Spaces -- Open Orbits -- The Cycle Space of a Flag Domain -- Cycle Spaces as Universal Domains -- Universal Domains -- B-Invariant 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 -- Analytic and Geometric Consequences -- The Double Fibration Transform -- Variation of Hodge Structure -- Cycles in the K3 Period Domain -- The Full Cycle Space -- Combinatorics of Normal Bundles of Base Cycles -- Methods for Computing H1(C; O) -- Classification for Simple with rank < rank -- Classification for rank = rank .

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.

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