Project/Area Number  10640035 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Algebra

Research Institution  TOKYO METOROPOLITAN UNIVERSITY 
Principal Investigator 
ト部 東介 都立大, 理学(系)研究科, 助教授 (70145655)
KURANO Kazuhiko Tokyo Metropolitan Univ., Dept of Math., AP, 理学研究科, 助教授 (90205188)

CoInvestigator(Kenkyūbuntansha) 
FUKUI Toshizumi Saitama Univ., Dept of Math. AP, 理学部, 助教授 (90218892)
ISHIKAWA Goo Hokkaido Univ., Dept of Math., AP, 理学研究科, 助教授 (50176161)
YOKURA Shoji Kagoshima Univ., Dept of Math., P, 理学部, 教授 (60182680)
OKA Mutsuo Dept of Math. P, 理学研究科, 教授 (40011697)
TREAO Hiroaki Dept of Math. P, 理学研究科, 教授 (90119058)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,300,000 (Direct Cost : ¥3,300,000)
Fiscal Year 1999 : ¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1998 : ¥1,800,000 (Direct Cost : ¥1,800,000)

Keywords  resolution of singularity / RiemannRoch / CohenMacaulayfication / singular variety / 特異点解消 / リーマン・ロッホ / コーエン・マコーレー化 / 特異多様体 / オルタレーション 
Research Abstract 
Our aim was to make resolution of singularities in arbitrary characteristic (or, more generally, in mixedcharacteristic). 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 GilletSoule. Using it, the positivity of Dutta multiplicity was proven, and if one of two module is CohenMacaulay over a Roberts ring of equicharacteristic, then the same result as Serre's positivity follows from it. Kawasaki proved the existence of CohenMacaulayfication for arbitrary schemes. By the result, we may assume that the given scheme is CohenMacaulay when we construct resolution of singularity. Ito constructed 3dimensional 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 FultonMacPherson. Ishikawa studied the tangent developables of space curves. Fukui proved the CohenMacaulayness for some rings that are important in sungularity theory.
