Overview
Presents in-depth surveys of topics in singularity theory, including connections with other subjects
Ideal for graduate students and newcomers to the area, and as a reference for specialists
Emphasizes clarity and quality of exposition rather than technical details
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Editors and Affiliations
About the editors
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 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.
Bibliographic Information
Book Title: Handbook of Geometry and Topology of Singularities IV
Editors: José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade
DOI: https://doi.org/10.1007/978-3-031-31925-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-31924-2Published: 08 October 2023
Softcover ISBN: 978-3-031-31927-3Due: 22 October 2024
eBook ISBN: 978-3-031-31925-9Published: 07 October 2023
Edition Number: 1
Number of Pages: XX, 608
Number of Illustrations: 6 b/w illustrations, 12 illustrations in colour
Topics: Topology, Algebraic Geometry, Analysis