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Compact Riemann Surfaces : International Inventory of Musical Sources. a - R. Narasimhan

Compact Riemann Surfaces

International Inventory of Musical Sources. a

Paperback Published: 1st September 1992
ISBN: 9783764327422
Number Of Pages: 122

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These notes form the contents of a Nachdiplomvorlesung given at the Forschungs- institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. K. Chandrasekharan and Prof. Jurgen Moser have encouraged me to write them up for inclusion in the series, published by Birkhiiuser, of notes of these courses at the ETH. Dr. Albert Stadler produced detailed notes of the first part of this course, and very intelligible class-room notes of the rest. Without this work of Dr. Stadler, these notes would not have been written. While I have changed some things (such as the proof of the Serre duality theorem, here done entirely in the spirit of Serre's original paper), the present notes follow Dr. Stadler's fairly closely. My original aim in giving the course was twofold. I wanted to present the basic theorems about the Jacobian from Riemann's own point of view. Given the Riemann-Roch theorem, if Riemann's methods are expressed in modern language, they differ very little (if at all) from the work of modern authors.

Algebraic functionsp. 3
Riemann surfacesp. 8
The sheaf of germs of holomorphic functionsp. 12
The Riemann surface of an algebraic functionp. 15
Sheavesp. 17
Vector bundles, line bundles and divisorsp. 27
Finiteness theoremsp. 32
The Dolbeault isomorphismp. 38
Weyl's lemma and the Serre duality theoremp. 43
The Riemann-Roch theorem and some applicationsp. 49
Further properties of compact Riemann surfacesp. 58
Hyperelliptic curves and the canonical mapp. 63
Some geometry of curves in projective spacep. 66
Bilinear relationsp. 77
The Jacobian and Abel's theoremp. 84
The Riemann theta functionp. 91
The theta divisorp. 97
Torelli's theoremp. 106
Riemann's theorem on the singularities of [Theta]p. 111
Referencesp. 119
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783764327422
ISBN-10: 3764327421
Series: International Inventory of Musical Sources. a
Audience: General
Format: Paperback
Language: English
Number Of Pages: 122
Published: 1st September 1992
Publisher: SPRINGER VERLAG GMBH
Country of Publication: CH
Dimensions (cm): 25.4 x 17.78  x 0.71
Weight (kg): 0.24