Resolution of singularities in arbitrary characteristic

解决任意特征中的奇点

• 批准号: 10640035
• 负责人: KURANO Kazuhiko
• 金额: $ 2.11万
• 依托单位: TOKYO METOROPOLITAN UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640035/
• 关键词: resolution of singularity; Riemann-Roch; Cohen-Macaulayfication; singular variety; オルタレーション

Our aim was to make resolution of singularities in arbitrary characteristic (or, more generally, in mixed-characteristic). By the help of the fund, investigators have got various results around the problem. Kurano described localized Chern characters in terms of Adams operations due to Gillet-Soule. Using it, the positivity of Dutta multiplicity was proven, and if one of two module is Cohen-Macaulay over a Roberts ring of equi-characteristic, then the same result as Serre's positivity follows from it. Kawasaki proved the existence of Cohen-Macaulayfication for arbitrary schemes. By the result, we may assume that the given scheme is Cohen-Macaulay when we construct resolution of singularity. Ito constructed 3-dimensional McKay correspondence. Oka studies flex curves using the method of resolution of singularities of toric varieties. Terao studied hyperplane arrangement by calculating monodromy. Nakamura studied how to compute explicit examples using computers. Takeda studied the standard conjecture due to Grothendieck. Yokura studied Milnor classes using equivariant theory due to Fulton-MacPherson. Ishikawa studied the tangent developables of space curves. Fukui proved the Cohen-Macaulayness for some rings that are important in sungularity theory.

我们的目标是解决任意特征（或者更一般地说，混合特征）中的奇异性。在该基金的帮助下，调查人员围绕这个问题取得了各种成果。仓野描述了本地化陈省身字符的亚当斯操作，由于吉列-Soule。利用它证明了Dutta重数的正性，证明了若Roberts环上的两个模之一是Cohen-Macaulay模，则可得到与Serre正性相同的结果.川崎证明了任意格式的Cohen-Macaulay化的存在性.利用这一结果，我们可以假定所给格式是Cohen-Macaulay格式。Ito构造了三维McKay对应。奥卡研究柔性曲线使用的方法的解决方案的奇异性的复曲面品种。寺尾研究超平面安排计算monodromy。中村研究如何计算明确的例子使用计算机。武田研究了格罗滕迪克提出的标准猜想。横仓研究米尔诺类使用等变理论由于富尔顿-麦克弗森。石川研究了空间曲线的切可展性。福井证明了一些环的Cohen-Macaulay性质，这些环在太阳性理论中很重要。

项目成果

T. Fukui: "Cohen-Macaulay properities of Thom-Boardman strata I : Morin's ideal"Proc. of London Math. Soc.. to appear.

T. Fukui：“Thom-Boardman 地层 I 的 Cohen-Macaulay 特性：莫林的理想”Proc。

T. Fukui: "Cohen-Macaulay properties of Thom-Boardman strata I: Morin's ideal"Proc. of London Math. Soc.. (to appear).

T. Fukui：“Thom-Boardman 地层 I 的 Cohen-Macaulay 特性：莫林的理想”Proc。

T.Fukui: "Cohen-Macaulay properties of Thom-Boardman strata I: Morin's ideal"Proc. of London Math. Soc.. (to appear).

T.Fukui：“Thom-Boardman 地层 I 的 Cohen-Macaulay 性质：莫林的理想”Proc。

K.Kurano: "Adams operations, localized Chern characters, and positivity Dutta multiplicity in characteristic 0"Trans. Amer. Math. Soc.. (to appear).

K.Kurano：“亚当斯运算、本地化的陈省身特征以及特征 0 中的正杜塔多重性”Trans。

K.Kurano: "The positivity of intersection multiplicities and symbolic powers of prime ideals" Compositio Math.to appear.

K.Kurano：“交叉多重性的正性和素理想的象征力量”Compositio Math. 出现。