Lectures on Riemann Surfaces, Jacobi Varieties - Brossura

Gunning, Robert C.

Brossura

ISBN 10: 0691619255 ISBN 13: 9780691619255

Casa editrice: Princeton Univ Pr, 2015

Riassunto

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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Dettagli dell'edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 0691619255
• ISBN 13: 9780691619255
• Rilegatura: Copertina flessibile
• Numero di pagine: 189
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile