Handbook of Geometry and Topology of Singularities IV
暫譯: 奇異性幾何與拓撲手冊 IV
Cisneros-Molina, José Luis, Dũng Tráng, Lê, Seade, José
相關主題
商品描述
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.
This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.
Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.
商品描述(中文翻譯)
這是《奇異性幾何與拓撲手冊》第四卷，該系列旨在提供該主題的最新進展、邊界及其與其他研究領域互動的易懂介紹。
本卷包含十二章，深入且易於閱讀地調查了奇異性理論的各種重要方面。其中一些主題補充了第一至第三卷中先前探討的內容。本卷研究的主題包括納什爆破（Nash blow up）、代數多樣體中的弧空間、行列式奇異性（determinantal singularities）、利普希茨幾何（Lipschitz geometry）、向量場和1-形式的指數、動機特徵類（motivic characteristic classes）、希爾伯特-薩繆爾重數（Hilbert-Samuel multiplicity）以及源自古典德拉姆複形（De Rham complex）的比較定理。
奇異性在數學和科學中無處不在。奇異性理論是一個熔爐，不同類型的數學問題在此互動，驚人的聯繫誕生，簡單的問題引發了在其他主題中共鳴的想法。這本書由世界專家撰寫，各種貢獻涵蓋了古典材料和現代發展，涉及一系列在基本上相互聯繫的主題。
本書適合研究生和初學者，以及可以將其作為指南的專家。
作者簡介
Lê Dũng Tráng (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975-1999) and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, and carousels, among other topics.
José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous Universityof Mexico. His research is in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor's fibration theorem for analytic maps. He was awarded the 2021 Solomon Lefschetz Medal by the Mathematical Council of the Americas.
作者簡介(中文翻譯)
何塞·路易斯·西斯內羅斯-莫利納（博士，華威大學 1999）是墨西哥國立自治大學數學研究所的研究員。他的研究興趣包括代數與微分拓撲、微分幾何和奇異性理論，特別專注於複數和實數解析映射的米爾諾纖維化的一般化。
黎長章（博士，巴黎大學 1969）是艾克斯-馬賽大學的名譽教授。之前他曾在巴黎第七大學（1975-1999）和馬賽大學任教，並擔任三里士提的國際理論物理中心數學部門負責人。他是現代奇異性理論的創始人之一，對於莫爾化、複數奇異性的拓撲、極點多樣體和旋轉木馬等主題做出了許多貢獻。
何塞·西德（博士，牛津大學 1980）是墨西哥國立自治大學數學研究所的全職研究員。他的研究集中在奇異多樣體的向量場指數和陳類的理論，並應用於葉狀結構以及米爾諾的解析映射纖維化定理。他於2021年獲得美洲數學委員會頒發的所羅門·萊夫謝茨獎章。
