黎曼曲面和热带曲线的模空间导引（英文版） [Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves] pdf epub mobi txt 电子书 下载 2025

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Lizhen，Ji，Eduard，Looijenga 著

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出版社： 高等教育出版社

ISBN：9787040474190

版次：1

商品编码：12065623

包装：精装

丛书名： Surveys of Modern Mathematics

外文名称：Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves

开本：16开

出版

内容简介

　　黎曼曲面及其模空间的概念由黎曼分别在其博士毕业论文和一篇著名的文章中定义。由于与数学和物理的许多学科联系广泛，黎曼曲面及其模空间得到了深入的研究，并将继续吸引人们的关注。近期热带曲线的研究迅速崛起。热带代数曲线是经典复数域上代数曲线以及黎曼曲面在热带半环上的一种模拟。
　　《黎曼曲面和热带曲线的模空间导引（英文版）》深入浅出地介绍了以上几个重要数学分支，并且重点强调如代数几何、复几何、双曲几何、拓扑、几何群理论和数学物理等不同学科之间的关联。季理真是美国密歇根大学教授，研究兴趣涉及几何、拓扑和分析领域，以及这些领域之间的联系，喜欢阅读和写作，曾获得Sloan研究奖。
　　Eduard Looijenga是世界代数几何学家之一，荷兰皇家艺术和科学院院士，现任教于清华大学。

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前言/序言

　　analogy with locally symmetric spaces， which by definition are obtained as orbit space of symmetric spaces endowed with an action of an arithmetic group. This analogy， though imperfect， has been very fruitful in the past decades， as it suggested both problems and solutions.
　　As we mentioned， compact Riemann surfaces can also be regarded as algebraic curves over the complex numbers. In the past few years， there has been an explosion of work on their tropical counterparts， i.e.， algebraic curves over the tropical semifield. These have appeared in many unexpected topics and make currently a very active area of study. It turns out that the moduli spaces of tropical curves also fit into the above analogy，in the sense that these are the orbit spaces of tropical Teichmuller spaces by outer automorphism groups of free groups. The outer automorphism groups of free groups are among the most important groups in geometric group theory， and the tropical Teichmuller spaces were studied as spaces of marked metric graphs before the subject of tropical geometry （and its name） existed.
　　Given the rich history of Riemann surfaces and their moduli spaces， and their generalizations， applications and connections with other subjects， it seems helpful to provide an accessible and timely introduction to all the above topics， while emphasizing the underlying connections. The current book is an attempt towards this goal. It consists of two parts. The first part deals with mapping class groups of surfaces， Teichmuller spaces and their applications to moduli spaces of Riemann surfaces， whereas the second part deals with tropical analogues and some applications in geometric group theory. Though these parts were conceived independently， together they cover both basic and essential results in these subjects as well as some recent developments. Although there exist several works on some of the above topics， we hope and believe that the nature of the subject justifies our offering of our own perspective on this wonderful world.

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塞尔老爷爷的著作，每一本都值得收藏。

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书表面很脏。：：。。一本白白的书，到我这竟然是黑色的

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李理论是表示论里的一大精髓，是算数几何不可缺少的理论。

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在知识海量的今天,这本书不一定有多高地位;但是能看完也就是一个胜利

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好书，内容更好值得购买，是正品

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书很好，物流也很快，很满意。

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讲述了微分流形和拓扑流形的结构的研究是现代数学的重要分支。随着20世纪50—60年代Milnor发现高维球面上的奇异微分结构和SmaIe证明了高维的Poincare猜想，流形拓扑学的研究进入了全新的领域，来自代数、代数拓扑和几何拓扑的诸多工具得到了广泛的应用。但是这也导致这一领域的文献较为分散和专门，不易被初学者所掌握。

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还没看，。。。。。。。。。

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书很好，S.S Chern的作品，内容毫无质疑。