1999 Fiscal Year Final Research Report Summary
Resolution of singularities in arbitrary characteristic
| Project/Area Number |
10640035
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | TOKYO METOROPOLITAN UNIVERSITY |
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Principal Investigator |
KURANO Kazuhiko Tokyo Metropolitan Univ., Dept of Math., AP, 理学研究科, 助教授 (90205188)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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)
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| Project Period (FY) |
1998 – 1999
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| Keywords | resolution of singularity / Riemann-Roch / Cohen-Macaulayfication / singular variety |
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| Research Abstract |
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.
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Research Products
(12 results)
