Handbook of Geometry and Topology of Singularities VIII
暫譯: 奇異性幾何與拓撲手冊 第八卷

Cisneros-Molina, José Luis, Dũng Tráng, Lê, Seade, José

Handbook of Geometry and Topology of Singularities VIII
  • 出版商: Springer
  • 出版日期: 2026-01-25
  • 售價: $7,360
  • 貴賓價: 9.5 折 $6,992
  • 語言: 英文
  • 頁數: 573
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031995708
  • ISBN-13: 9783031995705
  • 相關分類: 離散數學 Discrete-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

This is the eight volume of the Handbook of Geometry and Topology of Singularities, a series that provides 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 with reader-friendly introductions to several important topics and aspects of singularity theory, such as:

    Plane curve singularities studied by means of divides, which capture a lot of their topology. Viro's method to study the topology of real algebraic varieties, providing a wide range of possible combinations of topological and combinatorial invariants. Local tropicalization, a technique for attaching a combinatorial object to germs of subvarieties of algebraic tori and toric varieties. The theory of Zariski pairs and superisolated singularities. The McKay correspondence, a deep connection that links group theory, algebraic geometry, and representation theory. Calculations with Characteristic Cycles, a deep concept in the interplay between algebraic geometry, representation theory and microlocal analysis. The monodromy zeta functions in singularity theory. The singularities of the minimal model program of complex quasi-projective varieties. A general theory of Thom polynomials associated to the classification of map-germs. A discussion on indices and residues, intertwining the theories of complex analytic singular varieties and singular holomorphic foliations. The Monodromy in Integral Geometry and PDE. The topological theory of Hyperplane Arrangements.
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《奇異幾何與拓撲手冊》第八卷，這是一個提供該主題最新進展、前沿及其與其他研究領域互動的易讀性系列書籍。

本卷包含十二章，對幾個重要主題和奇異性理論的各個方面提供了友好的介紹，例如：

- 通過分割來研究平面曲線奇異性，這捕捉了它們的許多拓撲特徵。
- Viro 方法用於研究實代數多樣體的拓撲，提供了拓撲和組合不變量的多種可能組合。
- 局部熱帶化，一種將組合對象附加到代數圓環和錐多樣體的子多樣體的微小變化的技術。
- Zariski 對偶和超孤立奇異性的理論。
- McKay 對應，一個深刻的聯繫，將群論、代數幾何和表示論聯繫在一起。
- 特徵循環的計算，這是一個在代數幾何、表示論和微局部分析之間相互作用的深刻概念。
- 奇異性理論中的單調性 zeta 函數。
- 複數準射影多樣體的最小模型計劃的奇異性。
- 與映射微變的分類相關的 Thom 多項式的一般理論。
- 關於指數和殘差的討論，交織了複分析奇異多樣體和奇異全純葉簇的理論。
- 整數幾何和偏微分方程中的單調性。
- 超平面排列的拓撲理論。

本書適合研究生和新手學習該理論，也適合專家作為指南使用。

作者簡介

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests include Algebraic and Differential Topology, Differential Geometry, and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.

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 researcher at the Mathematics Institute of the National Autonomous University of 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. He is currently President of the Mexican Academy of Sciences.

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、微分幾何以及奇異性理論，特別專注於對於複數和實數解析映射的米爾諾纖維化的推廣。 黎長章（博士，巴黎大學 1969）是艾克斯-馬賽大學的名譽教授。之前他曾擔任巴黎第七大學（1975-1999）和馬賽大學的教授，並且是三藩市國際理論物理中心（ICTP）數學部門的負責人。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、極點變數以及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研究員。他的研究集中在奇異變數的向量場指數和陳類理論，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·勒夫謝茲獎章。目前他是墨西哥科學院的院長。

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