9781461259633 - lectures on riemann surfaces (graduate texts in mathematics, band 81) von forster, otto (2 Ergebnisse)
Sprache: Englisch
Verlag: Springer, 2011
- Softcover
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes KönigreichRia Christie Collections
Verkäufer/-in kontaktierenVerkäufer/-in mit 5 SternenZustand: Neu
EUR 79,61
EUR 14,00 VersandVersand von Vereinigtes Königreich nach USAAnzahl: Mehr als 20 verfügbar
Zustand: New. In.
Sprache: Englisch
Verlag: Springer New York, Springer New York, 2011
- Softcover
Anbieter: AHA-BUCH GmbH, Einbeck, DeutschlandAHA-BUCH GmbH
Verkäufer/-in kontaktierenVerkäufer/-in mit 5 SternenZustand: Neu
EUR 74,95
EUR 62,06 VersandVersand von Deutschland nach USAAnzahl: 1 verfügbar
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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-valued 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.
