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Lectures on Riemann Surfaces - Corrected third printing

Door Otto Forster

Categorie	Algemeen wetenschap
Boeknummer	#342308-ZA25
Titel	Lectures on Riemann Surfaces - Corrected third printing
Auteur	Forster, Otto
Boektype	Gebonden hardcover
Druk	253e druk
Uitgeverij	New York : Springer-Verlag
Jaar van uitgave	1991
ISBN10	0387906177
ISBN13	9780387906171
Taal	Engels
Beschrijving	Original boards, illustrated with numerous equations and diagrams, 8vo. Graduate Texts in Mathematics, 81.
Samenvatting	This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-value... (Lees verder)d behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations. The second chapter is devoted to compact Riemann surfaces. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle. The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz' Lemma.
Pagina's	254
Conditie	Goed — Spine slightly discoloured, name in pen on title page.
Prijs	€ 30,00

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