Lectures on Riemann Surfaces(Graduate Texts in Mathematics)

计算机科学技术基础学科

原   价:
1200
售   价:
960.00
优惠
平台大促 低至8折优惠
发货周期:外国库房发货,通常付款后3-5周到货
作      者
出  版 社
出版时间
1981年11月02日
装      帧
精装
ISBN
9780387906171
复制
页      码
256
开      本
语      种
英文
综合评分
暂无评分
我 要 买
- +
库存 47 本
  • 图书详情
  • 目次
  • 买家须知
  • 书评(0)
  • 权威书评(0)
图书简介
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.
馆藏图书馆
Princeton University Library
本书暂无推荐
本书暂无推荐
看了又看
  • 上一个
  • 下一个