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 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. 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.
By:
Shihoko Ishii
Imprint: Springer Verlag, Japan
Country of Publication: Japan
Edition: Softcover reprint of the original 2nd ed. 2018
Dimensions:
Height: 235mm,
Width: 155mm,
Spine: 13mm
Weight: 454g
ISBN: 9784431568711
ISBN 10: 4431568719
Pages: 236
Publication Date: 25 December 2018
Audience:
Professional and scholarly
,
Undergraduate
Format: Paperback
Publisher's Status: Active
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.
Shihoko Ishii is a professor emeritus at the University of Tokyo and a professor at the Tokyo Woman's Christian University.
