Compact Riemann Surfaces (lectures In Mathematics Eth Zurich Series)
by Raghavan Narasimhan /
1996 / English / PDF
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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.
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.
