Introduction To Singularities And Deformations
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Author |
: Gert-Martin Greuel |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 482 |
Release |
: 2007-02-23 |
ISBN-10 |
: 9783540284192 |
ISBN-13 |
: 3540284192 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Introduction to Singularities and Deformations by : Gert-Martin Greuel
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 |
: Jan Stevens |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 172 |
Release |
: 2003 |
ISBN-10 |
: 3540005609 |
ISBN-13 |
: 9783540005605 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Deformations of singularities by : Jan Stevens
Author |
: Shihoko Ishii |
Publisher |
: Springer |
Total Pages |
: 242 |
Release |
: 2018-09-21 |
ISBN-10 |
: 9784431568377 |
ISBN-13 |
: 4431568379 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Introduction to Singularities by : Shihoko Ishii
This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have 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. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. 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. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. 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. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.
Author |
: Edoardo Sernesi |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 343 |
Release |
: 2007-04-20 |
ISBN-10 |
: 9783540306153 |
ISBN-13 |
: 3540306153 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Deformations of Algebraic Schemes by : Edoardo Sernesi
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 |
: Peter Orlik |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 698 |
Release |
: 1983 |
ISBN-10 |
: 9780821814666 |
ISBN-13 |
: 0821814664 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Singularities, Part 2 by : Peter Orlik
On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This work presents the written versions of all but three of the invited talks presented at this Symposium. It contains 2 papers by invited speakers who aren't able to attend.
Author |
: Claude Sabbah |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 290 |
Release |
: 2007-12-20 |
ISBN-10 |
: 9781848000544 |
ISBN-13 |
: 1848000545 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Isomonodromic Deformations and Frobenius Manifolds by : Claude Sabbah
Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
Author |
: János Kollár |
Publisher |
: Cambridge University Press |
Total Pages |
: 381 |
Release |
: 2013-02-21 |
ISBN-10 |
: 9781107035348 |
ISBN-13 |
: 1107035341 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Singularities of the Minimal Model Program by : János Kollár
An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Author |
: Jean-paul Brasselet |
Publisher |
: World Scientific |
Total Pages |
: 917 |
Release |
: 2007-01-16 |
ISBN-10 |
: 9789814477048 |
ISBN-13 |
: 9814477044 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop by : Jean-paul Brasselet
Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Author |
: J. H. M. Steenbrink |
Publisher |
: |
Total Pages |
: 9 |
Release |
: 1985 |
ISBN-10 |
: OCLC:46010773 |
ISBN-13 |
: |
Rating |
: 4/5 (73 Downloads) |
Synopsis Deformations of Singularities by : J. H. M. Steenbrink
Author |
: Robin Hartshorne |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 241 |
Release |
: 2009-11-12 |
ISBN-10 |
: 9781441915962 |
ISBN-13 |
: 1441915966 |
Rating |
: 4/5 (62 Downloads) |
Synopsis Deformation Theory by : Robin Hartshorne
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.