Erschienen: 23.08.2016 Abbildung von Ishii | Introduction to Singularities | Softcover reprint of the original 1st ed. 2014 | 2016

Ishii

Introduction to Singularities

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Softcover reprint of the original 1st ed. 2014 2016. Buch. viii, 223 S. 102 s/w-Abbildungen, Bibliographien. Softcover

Springer. ISBN 9784431562610

Format (B x L): 15,5 x 23,5 cm

Gewicht: 361 g

In englischer Sprache

Produktbeschreibung

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.

Gesamtwerk

Die 8. Auflage ist wieder auf sechs Bände angelegt. Darin finden sich übersichtlich und in systematischer Gliederung Vertragsmuster aus der Feder erfahrener Experten. Jedem dieser Muster folgen Anmerkungen, mit denen der dem Vertragsentwurf zu Grunde liegende Sachverhalt und die Gründe für die Wahl des spezifischen Formulars erläutert werden.

Autoren

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