Those notes shape the contents of a Nachdiplomvorlesung given on the Forschungs institut fur Mathematik of the Eidgenossische Technische Hochschule, Zurich from November, 1984 to February, 1985. Prof. ok. Chandrasekharan and Prof. Jurgen Moser have inspired me to write down them up for inclusion within the sequence, released by means of Birkhiiuser, of notes of those classes on the ETH. Dr. Albert Stadler produced specified notes of the 1st a part of this path, and intensely intelligible class-room notes of the remainder. with out this paintings of Dr. Stadler, those notes don't have been written. whereas i've got replaced a few issues (such because the facts of the Serre duality theorem, the following performed solely within the spirit of Serre's unique paper), the current notes keep on with Dr. Stadler's quite heavily. My unique goal in giving the path was once twofold. i wished to offer the elemental theorems concerning the Jacobian from Riemann's personal perspective. Given the Riemann-Roch theorem, if Riemann's tools are expressed in glossy language, they vary little or no (if in any respect) from the paintings of recent authors.
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