Singularity Theory

Author: Vladimir Igorevich Arnolʹd
Publisher: Cambridge University Press
ISBN: 9780521285117
Format: PDF, ePub, Mobi
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Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.

Singularities of Plane Curves

Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
ISBN: 9780521789592
Format: PDF
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Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.

Maximal Cohen Macaulay Modules Over Cohen Macaulay Rings

Author: Y. Yoshino
Publisher: Cambridge University Press
ISBN: 9780521356947
Format: PDF, Mobi
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The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.

Isolated Singular Points on Complete Intersections

Author: Eduard Looijenga
Publisher: Cambridge University Press
ISBN: 0521286743
Format: PDF, Kindle
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This book will be of use to professional mathematicians working in algebraic geometry, complex-analytical geometry and, to some extent, differential analysis.

Lectures on the Ricci Flow

Author: Peter Topping
Publisher: Cambridge University Press
ISBN: 0521689473
Format: PDF, ePub
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An introduction to Ricci flow suitable for graduate students and research mathematicians.

Manifolds with Singularities and the Adams Novikov Spectral Sequence

Author: Boris I. Botvinnik
Publisher: Cambridge University Press
ISBN: 9780521426084
Format: PDF, ePub, Docs
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Traditionally, the Adams-Novikov spectral sequence has been a tool that has enabled the computation of generators and relations to describe homotopy groups. Here a natural geometric description of the sequence is given in terms of cobordism theory and manifolds with singularities. The author brings together many interesting results not widely known outside the USSR, including some recent work by Vershinin.

Lectures on Invariant Theory

Author: Igor Dolgachev
Publisher: Cambridge University Press
ISBN: 9780521525480
Format: PDF, Kindle
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The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

Singularities

Author: Jean-Paul Brasselet
Publisher: Cambridge University Press
ISBN: 9780521466318
Format: PDF, Docs
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This book contains papers given at the International Singularity Conference held in 1991 at Lille.