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Introduction to singularities

Ishii, Shihoko.

Introduction to singularities

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to singularitiesby Shihoko Ishii.
Author:	Ishii, Shihoko.
Published:	Tokyo :Springer Japan :2018.
Description:	x, 236 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Singularities (Mathematics)
Online resource:	https://doi.org/10.1007/978-4-431-56837-7
ISBN:	9784431568377$q(electronic bk.)

Introduction to singularities
Ishii, Shihoko.

Introduction to singularities[electronic resource] /by Shihoko Ishii. - 2nd ed. - Tokyo :Springer Japan :2018. - x, 236 p. :ill., digital ;24 cm.

1. Sheaves, algebraic varieties and analytic spaces -- 2. Homological algebra and duality -- 3. Singularities, algebraization and resolutions of singularities -- 4. Divisors on a variety and the corresponding sheaves -- 5. Differential forms around the singularities -- 6. Two dimensional singularities -- 7. Higher dimensional singularities -- 8. Deformations of singularities.

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 workDiscours 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. 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.

ISBN: 9784431568377$q(electronic bk.)

Standard No.: 10.1007/978-4-431-56837-7doiSubjects--Topical Terms:

185806
Singularities (Mathematics)

LC Class. No.: QA614.58 / .I845 2018

Dewey Class. No.: 514.746

Introduction to singularities
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505 0 $a 1. Sheaves, algebraic varieties and analytic spaces -- 2. Homological algebra and duality -- 3. Singularities, algebraization and resolutions of singularities -- 4. Divisors on a variety and the corresponding sheaves -- 5. Differential forms around the singularities -- 6. Two dimensional singularities -- 7. Higher dimensional singularities -- 8. Deformations of singularities.
520 $a 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 workDiscours 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. 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.
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650 2 4 $a Commutative Rings and Algebras. $3 274057
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