Deformation Theory

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 1441915966
Total Pages : 241 pages
Book Rating : 4.62/5 ( download)

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Download or read book Deformation Theory written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2009-11-12 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3540306153
Total Pages : 343 pages
Book Rating : 4.53/5 ( download)

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Download or read book Deformations of Algebraic Schemes written by Edoardo Sernesi and published by Springer Science & Business Media. This book was released on 2007-04-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Martin Markl
Publisher : American Mathematical Soc.
ISBN 13 : 0821889796
Total Pages : 129 pages
Book Rating : 4.94/5 ( download)

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Download or read book Deformation Theory of Algebras and Their Diagrams written by Martin Markl and published by American Mathematical Soc.. This book was released on 2012 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together both the classical and current aspects of deformation theory. The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. In the interest of readability, some technically complicated proofs have been omitted when a suitable reference was available. The relation between the uniform continuity of algebraic maps and topologized tensor products is explained in detail, however, as this subject does not seem to be commonly known and the literature is scarce. The exposition begins by recalling Gerstenhaber's classical theory for associative algebras. The focus then shifts to a homotopy-invariant setup of Maurer-Cartan moduli spaces. As an application, Kontsevich's approach to deformation quantization of Poisson manifolds is reviewed. Then, after a brief introduction to operads, a strongly homotopy Lie algebra governing deformations of (diagrams of) algebras of a given type is described, followed by examples and generalizations.

Author : Eivind Eriksen
Publisher : CRC Press
ISBN 13 : 1498796028
Total Pages : 242 pages
Book Rating : 4.26/5 ( download)

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Download or read book Noncommutative Deformation Theory written by Eivind Eriksen and published by CRC Press. This book was released on 2017-09-19 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gert-Martin Greuel
Publisher : Springer Science & Business Media
ISBN 13 : 3540284192
Total Pages : 482 pages
Book Rating : 4.92/5 ( download)

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Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel and published by Springer Science & Business Media. This book was released on 2007-02-23 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yüksel Altiner
Publisher : Springer Science & Business Media
ISBN 13 : 3662039354
Total Pages : 109 pages
Book Rating : 4.59/5 ( download)

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Download or read book Analytical Surface Deformation Theory written by Yüksel Altiner and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alexander R. Its
Publisher : Springer
ISBN 13 : 3540398236
Total Pages : 318 pages
Book Rating : 4.33/5 ( download)

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Download or read book The Isomonodromic Deformation Method in the Theory of Painleve Equations written by Alexander R. Its and published by Springer. This book was released on 2006-11-14 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 1441915958
Total Pages : 241 pages
Book Rating : 4.55/5 ( download)

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Download or read book Deformation Theory written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hossein Abbaspour
Publisher : Springer Science & Business Media
ISBN 13 : 3834896802
Total Pages : 174 pages
Book Rating : 4.03/5 ( download)

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Download or read book Deformation Spaces written by Hossein Abbaspour and published by Springer Science & Business Media. This book was released on 2010-04-21 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.

Author : Robert Millard Jones
Publisher : Bull Ridge Corporation
ISBN 13 : 0978722310
Total Pages : 641 pages
Book Rating : 4.19/5 ( download)

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Download or read book Deformation Theory of Plasticity written by Robert Millard Jones and published by Bull Ridge Corporation. This book was released on 2009 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: