Lectures on Riemann Surfaces, Jacobi Varieties

Gunning, R. C.

ISBN 10: 0691081271 / ISBN 13: 9780691081274

Edité par Princeton University Press / University of Tokyo Press, 1972

A propos de cet article

195 pp., Paperback, previous owner's name to the title page, else very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

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Détails bibliographiques

• Titre: Lectures on Riemann Surfaces, Jacobi Varieties
• Éditeur: Princeton University Press / University of Tokyo Press
• Date de parution: 1972
• Langue: anglais
• ISBN à 10 chiffres: 0691081271
• ISBN à 13 chiffres: 9780691081274
• Reliure: Couverture souple
• État de l'article: Very Good

A propos de ce titre

Synopsis

A sequel to Lectures on Riemann Surfaces (Mathematical Notes, 1966), this volume continues the discussion of the dimensions of spaces of holomorphic cross-sections of complex line bundles over compact Riemann surfaces. Whereas the earlier treatment was limited to results obtainable chiefly by one-dimensional methods, the more detailed analysis presented here requires the use of various properties of Jacobi varieties and of symmetric products of Riemann surfaces, and so serves as a further introduction to these topics as well.

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.

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