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Thursday, January 30, 2020 | History

11 edition of Introduction to Singularities and Deformations (Springer Monographs in Mathematics) found in the catalog.

Introduction to Singularities and Deformations (Springer Monographs in Mathematics)

  • 297 Want to read
  • 13 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Mathematics,
  • Science/Mathematics,
  • Geometry - Algebraic,
  • Complex space germs,
  • Equisingularity,
  • Local and semi-local rings,
  • Mathematics / Geometry / Algebraic,
  • Plane curve singularities,
  • Versal deformation,
  • Deformations of singularities,
  • Singularities (Mathematics)

  • The Physical Object
    FormatHardcover
    Number of Pages474
    ID Numbers
    Open LibraryOL9055847M
    ISBN 103540283803
    ISBN 109783540283805

    Higher dimensional singularities7. The focus is on an isolated singularity in an algebraic variety. 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. It includes complete proofs. Most of them were about non-singular varieties.

    By lifting upcovering singularities0. 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. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. Versal deformationsAppendix: Recent resultsReferences Informations sur le produit.

    In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. Elliptic singularities6. 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. The book includes many examples and exercises After its publication, research on algebraic varieties developed steadily. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced.


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Introduction to Singularities and Deformations book

Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties.

The text is clear and well written and it is accessible to non-expert readers. Algebraization theorem3. Singularities were considered "bad" objects that interfered with knowledge of the structure of an algebraic variety. The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.

The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry. First, mostly non-singular varieties were studied.

Sheaves on a topological space1. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.

The focus is on an isolated singularity in an algebraic variety. This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. It is a useful volume both for readers studying singular varieties for the first time and for experts on classification of singularities.

It is given with complete proofs, new in many cases. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.

Quitient singularities6. The focus is on an isolated singularity in an algebraic variety. Classification of two-dimensional singularities by 7. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation including non-uniform and anisotropic meshesmathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others.

This introductory text provides the general framework of the theory while still remaining concrete. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained.

Shustin: Introduction to Singularities and Deformations - hardcover ISBN: ID: 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.

More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. Elliptic singularities6.

Stable Mappings and Their Singularities

Computational aspects of the theory are discussed as well. This introductory text provides the general framework of the theory while still remaining concrete. Reviews From the reviews: "This monograph is dedicated to the theory of singularities, a subject with a central role in modern mathematics.

About this book Introduction 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.

Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings.

Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties.Download PDF Curves And Singularities A Geometrical Introduction To Singularity Theory book full free. Curves And Singularities A Geometrical Introduction To Singularity.

PDF Book Download Full PDF eBook Free Download (T Fukui and M Hasegawa)Involutive Deformations of the Regular Part of a Normal Surface (A Harris and K Miyajima)Connected. This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes.

In that book he introduced coordinates to the study of geometry. It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness.

Singular Problems in Shell Theory

Mar 17,  · In this memoir, it is shown that the parameter space for the versal deformation of an isolated singularity \((V,O)\) —whose existence was established by Grauert in —is isomorphic to the space associated to the link \(M\) of \(V\) by Kuranishi using the CR-geometry of \(M\).

singularities, behavior of these singularities under deformations and determine all these singularities of dimension up to 2. 1. Introduction In birational geometry, canonical, log canonical, terminal and log terminal singularities play important roles. These singularities are all normal Q-Gorenstein.

The speci c feature of the present Introduction to Singular-ities and Deformations, separating it from other introductions to singularity we did not restrict the book to that speci c purpose. treatment of equisingular deformations of plane curve singularities.

This is a new treatment, based on the theory of deformations of the.