# Introduction to Singularities

## Shihoko Ishii

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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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Professor Ishii is the first woman full professor in Mathematics Department of the University of Tokyo.

Review :

“This book presents some results of the study of singularities within the field of algebraic geometry. ... The text is clear and well written and it is accessible to non-expert readers. ... the author defines all the concepts and the results are either proved or a reference is provided. This makes the book self-contained in a broad sense. It is a useful volume both for readers studying singular varieties for the first time and for experts on classification of singularities.” (Santiago Encinas, Mathematical Reviews, August, 2015)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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## 1.INTRODUCTION TO SINGULARITIES

ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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## 2.INTRODUCTION TO SINGULARITIES

ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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## 3.Introduction to Singularities (Hardback)

Edité par Springer Verlag, Japan, Japan (2014)
ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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Description du livre Springer Verlag, Japan, Japan, 2014. Hardback. État : New. 2014 ed.. Language: Japanese,English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. 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 methode pour bien conduire sa raison, et chercher la verite 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. N° de réf. du libraire LIE9784431550808

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## 4.INTRODUCTION TO SINGULARITIES

ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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## 5.Introduction to Singularities (Hardback)

Edité par Springer Verlag, Japan, Japan (2014)
ISBN 10 : 4431550801 ISBN 13 : 9784431550808
Neuf(s) Couverture rigide Quantité : 1
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Description du livre Springer Verlag, Japan, Japan, 2014. Hardback. État : New. 2014 ed.. Language: Japanese,English . Brand New Book. 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 methode pour bien conduire sa raison, et chercher la verite 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. N° de réf. du libraire AAW9784431550808

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## 6.Introduction to Singularities (Hardback)

Edité par Springer Verlag, Japan, Japan (2014)
ISBN 10 : 4431550801 ISBN 13 : 9784431550808
Neuf(s) Couverture rigide Quantité : 1
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Description du livre Springer Verlag, Japan, Japan, 2014. Hardback. État : New. 2014 ed.. Language: Japanese,English . Brand New Book. 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 methode pour bien conduire sa raison, et chercher la verite 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. N° de réf. du libraire AAW9784431550808

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## 7.Introduction to Singularities

Edité par Springer Verlag, Japan (2014)
ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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## 8.Introduction to Singularities

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## 9.Introduction to Singularities

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ISBN 10 : 4431550801 ISBN 13 : 9784431550808
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## 10.Introduction to Singularities

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