Classification of higher dimensional hypersurface singularities in terms of non-degenerate complete intersections

根据非简并完全交集对高维超曲面奇点进行分类

基本信息

批准号：
12640020
负责人：
TOMARI Masataka
金额：
$ 2.05万
依托单位：
Kanazawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

On the main theme of this project :(1) In 2000, M. Tomari studied the nitration of ideals on terminal singularities where the associated graded rings are integral domains with isolated singularity. As a special case, he showed the regularity of their associated graded rings of 3-dimensional regular local ring. In 1 2001, Tomari gave an inequality about Milnor number μ(f) of a hypersurface isolated singularity Uin terms of weighted Taylor expansion of the defining equation f. Here the equality holds iiand only if the initial form defines an isolated singularity. This gives a characterization of a semiquasi-homogeneous condition in terms of μ. The proof uses a result of Tomari on multiplicity of filtered ring.(2) T. Hayakawa studied several partial resolutions of 3-dimensipnal terminal singularities with index is not less than two. In 2000, he constructed an interesting example which admits a partial resolution where at worst Gorenstein terminal singularities remain. This was understood naturally by the' studies of the special partial resolution of rational double points which appears as the general members of anti-canonical linear system of the singularity. In 2001 he also studied the irreducible components of this type of partial resolution.As related-works on complex analysis :(3) H. Fujimoto had succeeded to construct a new series of examples of hyperbolic hypersurfaces of degree 2^n in n-dimensional complex protective spaces. In the case of n = 2, this example gives the world record of the minimal possible degree of the ambient spaces for such situation.(4) A. Kodama studied the general ellipsoids with not necessary smooth boundaries from the points of view of the Webster metric.

在该项目的主题上：（1）在2000年，托马里·托马里（M. Tomari）研究了对终端奇异性的硝化，其中相关的分级环是具有孤立奇异性的整体域。作为一个特殊情况，他展示了其相关的3维常规局部环的定期性。在2001年1月1日，托马里（Tomari）对定义方程式f的加权泰勒（Taylor）膨胀的高度表面分离的奇异性术语的不等式μ（f）。在这里，仅当初始形式定义孤立的奇点时，平等才能保持IIAND。这给出了半quassi均匀状态的表征。该证明使用Tomari的结果对多种过滤环。（2）T。hayakawa studiod具有索引的三端末端奇异性的几个部分分辨率不少于两个。在2000年，他构建了一个有趣的例子，该例子承认了部分决议，在最坏的戈伦斯坦终端奇异点仍然存在。通过对理性双点的特殊部分解决的研究，自然而然地理解了这一点，这些分辨率似乎是奇异性抗传统线性系统的一般成员。在2001年，他还研究了这种类型的部分分辨率的不可还原组成部分。作为复杂分析的相关工作：（3）H。Fujimoto成功地构建了N维复杂的Space中N维型2^n的双曲超曲面的一系列新示例。在n = 2的情况下，此示例给出了这种情况的世界记录。（4）A。Kodama从Webster Metric的角度来看，将一般椭圆形的一般椭圆形研究带有不必要的平滑边界。