Titlebook: Introduction to Singularities; Shihoko Ishii Textbook 2018Latest edition Springer Japan KK, part of Springer Nature 2018 Canonical divisor

小母马

Homological Algebra and Duality,In this chapter, we introduce cohomology groups by means of injective resolutions and show the duality theorem and spectral sequences. Readers who already know these concepts can skip this chapter.

雄伟

Normal 2-Dimensional Singularities,In this chapter we consider normal singularities of 2-dimensional varieties over .. A 2-dimensional integral algebraic variety is called a .. A normal singularity on a surface is an isolated singularity and by Corollary 3.5.17 it is a Cohen–Macauley singularity.

Orgasm

RACE

Deformations of Singularities,In this chapter we study deformations of singularities by varying parameters. In any deformations, singularities deform under certain orders. We will see this in Sect. ., and in Sect. . we will see that there exists a big deformation which contains every deformation. We assume that the varieties are defined over ..

毗邻

妨碍

Differential Forms Around a Singularity,e. By this consideration, plurigenera of isolated singularities are defined and the order of growth of the plurigenera gives a rough classification of isolated singularities. Here, a variety is always integral and defined over the complex number field ..

观点

Quick Overview of Recent Developments on Singularities,f this book. The goal of the chapter is just to show the directions of the research which is now going on. The reader who would like to step further in these directions is recommended to read some of the references cited in this chapter.

intrigue

Textbook 2018Latest edition 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 result

single

exclusice

Definition of a Singularity, Resolutions of Singularities, a field of characteristic zero has a resolution of the singularities. In this book our interest is focused on singularities. To this end, we study the resolved space instead of studying the singularity itself, therefore this resolution theorem is essential.