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Greuel, Gert-Martin; Lossen, Christoph; Shustin, Eugenii - Introduction to Singularities and Deformations - 9783540283805 - V9783540283805
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Introduction to Singularities and Deformations

€ 152.33
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Description for Introduction to Singularities and Deformations Hardback. Presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. This introductory text provides the general framework of the theory. It develops the relevant techniques, including the Weierstrass preparation theorem and the finite coherence theorem. Series: Springer Monographs in Mathematics. Num Pages: 484 pages, 54 black & white illustrations, biography. BIC Classification: PB. Category: (UU) Undergraduate. Dimension: 235 x 163 x 34. Weight in Grams: 840.

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.

This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory ... Read more

In the first part of the book the authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained.

The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thuscan serve as source for special courses in singularity theory and local algebraic and analytic geometry.

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Product Details

Format
Hardback
Publication date
2006
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Number of pages
484
Condition
New
Series
Springer Monographs in Mathematics
Number of Pages
472
Place of Publication
Berlin, Germany
ISBN
9783540283805
SKU
V9783540283805
Shipping Time
Usually ships in 15 to 20 working days
Ref
99-15

Reviews for Introduction to Singularities and Deformations
From the reviews: "This monograph is dedicated to the theory of singularities, a subject with a central role in modern mathematics. … This very well written book has a unified point of view based on the theory of analytic spaces, which allows a coherent presentation of both of its main themes: the theory of singularities ... Read more

Goodreads reviews for Introduction to Singularities and Deformations


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