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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.

（1）2000年，M.托马里研究了终端奇点上理想的硝化，其中相关的分次环是具有孤立奇点的整环。作为特例，他证明了三维正则局部环的相关分次环的正则性。2001年1月，托马里利用定义方程f的加权泰勒展开给出了关于超曲面孤立奇点U的Milnor数μ（f）的一个不等式.这里等式成立，且仅当初始形式定义了一个孤立奇点。这给出了关于μ的半拟齐次条件的特征。证明使用了托马里关于滤环重数的一个结果。(2)T. Hayakawa研究了指数不小于2的三维终端奇点的几种部分分解。在2000年，他构造了一个有趣的例子，承认部分决议，在最坏的Gorenstein终端奇点仍然存在。这一点在研究作为奇异反正则线性系统一般成员的有理二重点的特殊部分分解时得到了自然的理解。2001年他还研究了这类部分分解的不可约分支。藤本成功地在n维复保护空间中构造了一系列2^n次双曲超曲面的新例子。在n = 2的情况下，这个例子给出了这种情况下周围空间的最小可能度的世界纪录。(4)A.儿玉研究了一般的椭球没有必要光滑边界的观点的韦伯斯特度量。