Introduction to Singularities

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Introduction to Singularities by Shihoko Ishii, Springer Japan
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Shihoko Ishii ISBN: 9784431550815
Publisher: Springer Japan Publication: November 19, 2014
Imprint: Springer Language: English
Author: Shihoko Ishii
ISBN: 9784431550815
Publisher: Springer Japan
Publication: November 19, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Japan

Cover of the book Dynamics of Learning in Neanderthals and Modern Humans Volume 2 by Shihoko Ishii
Cover of the book Zero-Carbon Energy Kyoto 2012 by Shihoko Ishii
Cover of the book Semaphorins by Shihoko Ishii
Cover of the book Immunotherapy of Cancer by Shihoko Ishii
Cover of the book Advances in Vision Research, Volume I by Shihoko Ishii
Cover of the book Mechanism of Artificial Heart by Shihoko Ishii
Cover of the book Computing and Monitoring in Anesthesia and Intensive Care by Shihoko Ishii
Cover of the book Large A.C. Machines by Shihoko Ishii
Cover of the book HCV/Oxidative Stress and Liver Disease by Shihoko Ishii
Cover of the book Neurally Based Measurement and Evaluation of Environmental Noise by Shihoko Ishii
Cover of the book Protection of the Three Poles by Shihoko Ishii
Cover of the book Zero-Carbon Energy Kyoto 2010 by Shihoko Ishii
Cover of the book Computational Electrophysiology by Shihoko Ishii
Cover of the book Iron-Catalyzed Synthesis of Fused Aromatic Compounds via C–H Bond Activation by Shihoko Ishii
Cover of the book Community Seed Production Sustainability in Rice-Wheat Farming by Shihoko Ishii
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy