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Compact Riemann Surfaces (Paperback, 1992 ed.)
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Compact Riemann Surfaces (Paperback, 1992 ed.)
Series: Lectures in Mathematics. ETH Zurich
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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."
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