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Special Values of Automorphic Cohomology Classes
 
Mark Green University of California, Los Angeles
Phillip Griffiths Institute for Advanced Study, Princeton, New Jersey
Matt Kerr Washington University in St. Louis, St. Louis , Missouri
Special Values of Automorphic Cohomology Classes
eBook ISBN:  978-1-4704-1724-6
Product Code:  MEMO/231/1088.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
Special Values of Automorphic Cohomology Classes
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Special Values of Automorphic Cohomology Classes
Mark Green University of California, Los Angeles
Phillip Griffiths Institute for Advanced Study, Princeton, New Jersey
Matt Kerr Washington University in St. Louis, St. Louis , Missouri
eBook ISBN:  978-1-4704-1724-6
Product Code:  MEMO/231/1088.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2312014; 145 pp
    MSC: Primary 14; 22; 32;

    The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains \(D\) which occur as open \(G(\mathbb{R})\)-orbits in the flag varieties for \(G=SU(2,1)\) and \(Sp(4)\), regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces \(\mathcal{W}\) give rise to Penrose transforms between the cohomologies \(H^{q}(D,L)\) of distinct such orbits with coefficients in homogeneous line bundles.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. Geometry of the Mumford-Tate domains
    • 2. Homogeneous line bundles over the Mumford-Tate domains
    • 3. Correspondence and cycle spaces; Penrose transforms
    • 4. The Penrose transform in the automorphic case and the main result
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2312014; 145 pp
MSC: Primary 14; 22; 32;

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains \(D\) which occur as open \(G(\mathbb{R})\)-orbits in the flag varieties for \(G=SU(2,1)\) and \(Sp(4)\), regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces \(\mathcal{W}\) give rise to Penrose transforms between the cohomologies \(H^{q}(D,L)\) of distinct such orbits with coefficients in homogeneous line bundles.

  • Chapters
  • Introduction
  • 1. Geometry of the Mumford-Tate domains
  • 2. Homogeneous line bundles over the Mumford-Tate domains
  • 3. Correspondence and cycle spaces; Penrose transforms
  • 4. The Penrose transform in the automorphic case and the main result
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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