Singularities of Mappings
The Local Behaviour of Smooth and Complex Analytic Mappings
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Beschreibung
The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.
Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic.
By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.
Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic.
By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material,make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
Provides a self-contained introduction to the theory of singularities of mappings and ends at the frontier of current research Includes hundreds of exercises, with many designed to help master techniques of calculation A self-contained reference with 5 appendices on background material
Autor*in
David Mond
Themen in »Singularities of Mappings«
singularity theory Multiplicity Milnor-Tjurina relation vanishing homology left-right equivalence Finite determinancy Image and discriminant Multiple point spaces
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“Exercises at the end of each section are intended to help the interested reader to study the material in depth. … In general, this book is a nice supplement to the classical and modern monographs devoted to various sides of singularity theory. It comprises a lot of material scattered throughout numerous papers and presents it in a systematic and rigorous way. No doubt, it will become a common reference for various issues covered in this book.” (Eugenii Shustin, Mathematical Reviews, January, 2023)
“The book is written in a clear pedagogical style; it contains many examples, exercises, comments, remarks, nice pictures, very useful instructive and systematic references, computational algorithms with implementation in the computer algebra software systems Macaulay 2 and Mathematica, etc. … Without a doubt, the book is understandable, interesting and useful for graduate students and can serve as a good starting point for those who are interested in various aspects of both pure and applied mathematics.” (Aleksandr G. Aleksandrov, zbMATH 1448.58032, 2020)
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