Tweet | ## Lectures on Riemann Surfaces: |

A sequel to The first chapter consists of a rather explicit description of a canonical basis for the Abelian differentials on a marked Riemann surface, and of the description of the canonical meromorphic differentials and the prime function of a marked Riemann surface. Chapter 2 treats Jacobi varieties of compact Riemann surfaces and various subvarieties that arise in determining the dimensions of spaces of holomorphic cross-sections of complex line bundles. In Chapter 3, the author discusses the relations between Jacobi varieties and symmetric products of Riemann surfaces relevant to the determination of dimensions of spaces of holomorphic cross-sections of complex line bundles. The final chapter derives Torelli's theorem following A. Weil, but in an analytical context. Originally published in 1973. The - Frontmatter, pg. i
- Preface, pg. iii
- Contents, pg. vii
- § 1. Marked Riemann surfaces and their canonical differentials, pg. 1
- § 2. Jacobi varieties and their distinguished subvarieties, pg. 34
- § 3. Jacobi varieties and symmetric products of Riemann surfaces, pg. 72
- § 4. Intersections in Jacobi varieties and Torelli’s theorem, pg. 141
- Appendix. On conditions ensuring that W2r≠ ⌀, pg. 177
- Index of symbols, pg. 188
- Index, pg. 189
- Lectures on Complex Analytic Varieties (MN-14): Finite Analytic Mappings. (MN-14). [Hardcover and Paperback]
- Lectures on Modular Forms. (AM-48). [Paperback]
- Lectures on Vector Bundles over Riemann Surfaces. (MN-6). [Paperback]
- On Uniformization of Complex Manifolds: The Role of Connections (MN-22). [Hardcover and Paperback]
- Problems in Analysis: A Symposium in Honor of Salomon Bochner (PMS-31). [Hardcover and Paperback]
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