Deformation Theory

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 43,9 Mb
Release : 2009-11-12
Category : Mathematics
ISBN : 9781441915962

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Deformation Theory by Robin Hartshorne Pdf

The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.

Author : Edoardo Sernesi
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 44,7 Mb
Release : 2007-04-20
Category : Mathematics
ISBN : 9783540306153

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Deformations of Algebraic Schemes by Edoardo Sernesi Pdf

This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.

Author : Eivind Eriksen,Olav Arnfinn Laudal,Arvid Siqveland
Publisher : CRC Press
Page : 211 pages
File Size : 48,5 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781351652124

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Noncommutative Deformation Theory by Eivind Eriksen,Olav Arnfinn Laudal,Arvid Siqveland Pdf

Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 55,5 Mb
Release : 2009-12-10
Category : Mathematics
ISBN : 9781441915955

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Deformation Theory by Robin Hartshorne Pdf

The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.

Author : Robert Millard Jones
Publisher : Bull Ridge Corporation
Page : 641 pages
File Size : 50,8 Mb
Release : 2009
Category : Deformations (Mechanics)
ISBN : 9780978722319

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Deformation Theory of Plasticity by Robert Millard Jones Pdf

Author : Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 51,9 Mb
Release : 2007-02-23
Category : Mathematics
ISBN : 9783540284192

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Introduction to Singularities and Deformations by Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin Pdf

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many 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. It includes complete proofs.

Author : Alexander R. Its,Victor Y. Novokshenov
Publisher : Springer
Page : 318 pages
File Size : 42,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540398233

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The Isomonodromic Deformation Method in the Theory of Painleve Equations by Alexander R. Its,Victor Y. Novokshenov Pdf

Author : Yüksel Altiner
Publisher : Springer Science & Business Media
Page : 109 pages
File Size : 55,5 Mb
Release : 2013-04-18
Category : Science
ISBN : 9783662039359

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Analytical Surface Deformation Theory by Yüksel Altiner Pdf

Due to plate motions, tidal effects of the Moon and the Sun, atmosphe ric, hydrological, ocean loading and local geological processes, and due to the rotation of the Earth, all points on the Earth's crust are sub ject to deformation. Global plate motion models, based on the ocean floor spreading rates, transform fault azimuths, and earthquake slip vectors, describe average plate motions for a time period of the past few million years. Therefore, the investigation of present-day tectonic activities by global plate motion models in a small area with complex movements cannot supply satisfactory results. The contribution of space techniques [Very Long Baseline Interferome try (VLBI); Satellite Laser Ranging (SLR); Global Positioning System (GPS)] applied to the present-day deformations ofthe Earth's surface and plate tectonics has increased during the last 20 to 25 years. Today one is able to determine by these methods the relative motions in the em to sub-em-range between points far away from each other.

Author : Eivind Eriksen,Olav Arnfinn Laudal,Arvid Siqveland
Publisher : CRC Press
Page : 242 pages
File Size : 47,5 Mb
Release : 2017-09-19
Category : Mathematics
ISBN : 9781498796026

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Noncommutative Deformation Theory by Eivind Eriksen,Olav Arnfinn Laudal,Arvid Siqveland Pdf

Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. An essential part of this theory is the study of obstructions of liftings of representations using generalised (matric) Massey products. Suitable for researchers in algebraic geometry and mathematical physics interested in the workings of noncommutative algebraic geometry, it may also be useful for advanced graduate students in these fields.

Author : Michiel Hazewinkel,Murray Gerstenhaber
Publisher : Springer Science & Business Media
Page : 1024 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400930575

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Deformation Theory of Algebras and Structures and Applications by Michiel Hazewinkel,Murray Gerstenhaber Pdf

This volume is a result of a meeting which took place in June 1986 at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting. In particular it is now abundantly clear that the Deformation theory of algebras is indeed central to the whole philosophy of deformations/perturbations/stability. This is one of the main results of the 254 page paper below (practically a book in itself) by Gerstenhaber and Shack entitled "Algebraic cohomology and defor mation theory". Two of the main philosphical-methodological pillars on which deformation theory rests are the fol lowing • (Pure) To study a highly complicated object, it is fruitful to study the ways in which it can arise as a limit of a family of simpler objects: "the unraveling of complicated structures" . • (Applied) If a mathematical model is to be applied to the real world there will usually be such things as coefficients which are imperfectly known. Thus it is important to know how the behaviour of a model changes as it is perturbed (deformed).

Author : Vladimir Dotsenko,Sergey Shadrin,Bruno Vallette
Publisher : Cambridge University Press
Page : 187 pages
File Size : 52,7 Mb
Release : 2023-08-31
Category : Mathematics
ISBN : 9781108965644

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Maurer–Cartan Methods in Deformation Theory by Vladimir Dotsenko,Sergey Shadrin,Bruno Vallette Pdf

Covering an exceptional range of topics, this text provides a unique overview of the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.

Author : Ali Baklouti
Publisher : Walter de Gruyter GmbH & Co KG
Page : 379 pages
File Size : 48,9 Mb
Release : 2022-07-05
Category : Mathematics
ISBN : 9783110765397

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Deformation Theory of Discontinuous Groups by Ali Baklouti Pdf

This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.

Author : Victor Guillemin,Shlomo Sternberg
Publisher : American Mathematical Soc.
Page : 80 pages
File Size : 51,9 Mb
Release : 1966
Category : Mathematics
ISBN : 9780821812648

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Deformation Theory of Pseudogroup Structures by Victor Guillemin,Shlomo Sternberg Pdf

Author : Murray Gerstenhaber
Publisher : American Mathematical Soc.
Page : 377 pages
File Size : 42,8 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851418

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Deformation Theory and Quantum Groups with Applications to Mathematical Physics by Murray Gerstenhaber Pdf

Quantum groups are not groups at all, but special kinds of Hopf algebras of which the most important are closely related to Lie groups and play a central role in the statistical and wave mechanics of Baxter and Yang. Those occurring physically can be studied as essentially algebraic and closely related to the deformation theory of algebras (commutative, Lie, Hopf, and so on). One of the oldest forms of algebraic quantization amounts to the study of deformations of a commutative algebra $A$ (of classical observables) to a noncommutative algebra $A_h$ (of operators) with the infinitesimal deformation given by a Poisson bracket on the original algebra $A$. This volume grew out of an AMS-IMS-SIAM Joint Summer Research Conference, held in June 1990 at the University of Massachusetts at Amherst. The conference brought together leading researchers in the several areas mentioned and in areas such as ``$q$ special functions'', which have their origins in the last century but whose relevance to modern physics has only recently been understood. Among the advances taking place during the conference was Majid's reconstruction theorem for Drinfeld's quasi-Hopf algebras. Readers will appreciate this snapshot of some of the latest developments in the mathematics of quantum groups and deformation theory.

Author : Marco Manetti
Publisher : Springer Nature
Page : 576 pages
File Size : 47,7 Mb
Release : 2022-08-01
Category : Mathematics
ISBN : 9789811911859

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Lie Methods in Deformation Theory by Marco Manetti Pdf

This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.