# Introduction to Singularities and Deformations

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 is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete.

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 thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.

No Other Mirrors, Please!

Keep2Share

Oboom

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 is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete.

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 thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.

No Other Mirrors, Please!

Keep2Share

Oboom

**Related books**

- Introduction to Singularities and Deformations
- Plane Algebraic Curves: Translated by John Stillwell
- Algebraic Operads
- Topics in Geometry, Coding Theory and Cryptography (Algebra and Applications) by Arnaldo Garcia
- Algebraic Geometry in Coding Theory and Cryptography
- Multiplicative Invariant Theory
- Multiplicative Invariant Theory
- Qualitative Theory of Control Systems
- Qualitative Theory of Control Systems
- Abelian Varieties

## Random books

- Microsoft SharePoint 2010 Administrator's Companion
- How To Read Hands At No-Limit Hold'em
- Arne Dahl - Bußestunde
- The Words and Music of Sting by Christopher Gable
- Computational mathematics: Models, methods, and analysis with MATLAB and MPI by Robert E. White
- Getting Started with Simulink
- We Were Soldiers Once...and Young: Ia Drang - The Battle That Changed the War in Vietnam
- The Templar Code For Dummies
- McGraw-Hill Dictionary of Environmental Science & Technology
- Accounting for Non-Accounting Students
- Paese che vai... detto che trovi! Frasi idiomatiche in cinque lingue di Mary Gislon e Rosetta Palazzi
- Leslie Thomas - Waiting for the Day
- An Atlas of Diseases of the Nail
- Tinseltown: Murder, Morphine, and Madness at the Dawn of Hollywood [Audiobook]
- Cross-Calibration of Far UV Spectra of Solar System Objects and the Heliosphere

## Top books

- Behind the Smile: The Working Lives of Caribbean Tourism
- What the Most Successful People Do Before Breakfast: A Short Guide to Making Over Your Mornings - and Life
- Facebook Ads 101
- Kentucky Bourbon: The Early Years of Whiskeymaking
- Sex Offender Laws: Failed Policies, New Directions
- Open Geometry: OpenGL + Advanced Geometry
- Confident Ruby: 32 Patterns for Joyful Coding
- Intelligent Control Systems with LabVIEW
- Hollywood Said No! : Orphaned Film Scripts, Bastard Scenes, and Abandoned Darlings from the Creators of 'Mr. Show' (Audiobook)
- Magic - The Complete Course by Joshua Jay
- Complex Fractures of the Limbs: Diagnosis and Management
- Projektorganisation und Management im Software Engineering
- Upstairs at the White House: My Life with the First Ladies [Audiobook]
- Video2Brain - Office 365: SharePoint-Anwendungsfälle
- The Pursuit of Happiness: An Economy of Well-Being (Brookings Focus)

## Today books

- Enabling Manufacturing Competitiveness and Economic Sustainability
- 50 Architecture Ideas You Really Need to Know
- A Walk in the Woods: Rediscovering America on the Appalachian Trail
- Patent It Yourself: Your Step-by-Step Guide to Filing at the U.S. Patent Office, 15 edition
- Economic Methodology: A Historical Introduction
- Vue 7: From the ground up
- Field Free Line Magnetic Particle Imaging
- The Facts on File Space and Astronomy Handbook, Revised Edition
- Lehr- und Übungsbuch der deutschen Grammatik - aktuell: Lehrbuch, Testheft und Lösungsschlüssel
- Kristin Gore - Und wovon träumst du nachts?
- Professionelles Projektmanagement: Die besten Projekte, die erfolgreichsten Methoden, 2 Auflage
- Dressage for the Not-So-Perfect Horse: Riding Through the Levels on the Peculiar, Opinionated, Complicated Mounts We All Love
- Learning Adobe Dreamweaver CS6 Video Training
- celebraTORI: Unleashing Your Inner Party Planner to Entertain Friends and Family
- Essentials of Applied Dynamic Analysis