Titlebook: Introduction to Singularities; Shihoko Ishii Textbook 20141st edition Springer Japan 2014 Canonical divisors.Classification of singulariti

Awning

unstable-angina

addition

Sheaves, Algebraic Varieties and Analytic Spaces,In this chapter we introduce the concept of sheaves and introduce briefly algebraic varieties and analytic spaces which are in our interest. Readers who know these concepts well can skip this chapter.

陈列

frugal

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

Spinous-Process

Higher-Dimensional Singularities,A singularity of dimension higher than 2 is called a higher-dimensional singularity. In this section we mostly discuss higher-dimensional singularities. Unless otherwise stated, singularities are always of dimension . ≥ 2. Varieties are all integral algebraic varieties over . and the singularities considered are on such varieties.

戏法

我吃花盘旋

predict

Shihoko Ishiielated with the political, economic and social aims of the community in question, which are in turn influenced by global events. This review concentrates on the processes, aims, goals and research methods used by language planners. For fuller treatment of language planning theory and its educational

coddle

Shihoko Ishiidge of the linguistic code as well as of the socio-cultural rules, norms and values which guide the conduct and interpretation of speech and other channels of communication in a community. The ethnography of speaking or the ethnography of communication, as it was later referred to, is concerned with