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Author : Jan Stevens
Release : 2003
Genre : Deformations of singularities
Kind : eBook
Book Rating : 605/5 ( reviews)
Book Synopsis Deformations of singularities by : Jan Stevens
Download or read book Deformations of singularities written by Jan Stevens. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gert-Martin Greuel
Release : 2007-02-23
Genre : Mathematics
Kind : eBook
Book Rating : 192/5 ( reviews)
Book Synopsis Introduction to Singularities and Deformations by : Gert-Martin Greuel
Download or read book Introduction to Singularities and Deformations written by Gert-Martin Greuel. This book was released on 2007-02-23. 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 : Andras Némethi
Release : 2014-01-24
Genre : Mathematics
Kind : eBook
Book Rating : 311/5 ( reviews)
Book Synopsis Deformations of Surface Singularities by : Andras Némethi
Download or read book Deformations of Surface Singularities written by Andras Némethi. This book was released on 2014-01-24. Available in PDF, EPUB and Kindle. Book excerpt: The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several open problems. Recently several connections were established with low dimensional topology, symplectic geometry and theory of Stein fillings. This created an intense mathematical activity with spectacular bridges between the two areas. The theory of deformation of singularities is the key object in these connections.
Author : Shihoko Ishii
Release : 2014-11-19
Genre : Mathematics
Kind : eBook
Book Rating : 81X/5 ( reviews)
Book Synopsis Introduction to Singularities by : Shihoko Ishii
Download or read book Introduction to Singularities written by Shihoko Ishii. This book was released on 2014-11-19. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry 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. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. 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. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. 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-dim ensional 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.
Author : Michael Artin
Release : 1976
Genre : Deformations of singularities
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Lectures on Deformations of Singularities by : Michael Artin
Download or read book Lectures on Deformations of Singularities written by Michael Artin. This book was released on 1976. Available in PDF, EPUB and Kindle. Book excerpt:
