| 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 |
| 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 231; 2014; 145 ppMSC: 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.
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Table of Contents
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Chapters
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Introduction
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1. Geometry of the Mumford-Tate domains
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2. Homogeneous line bundles over the Mumford-Tate domains
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3. Correspondence and cycle spaces; Penrose transforms
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4. The Penrose transform in the automorphic case and the main result
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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
