Classification of isolated singularities by means of algebraic geometric studies of invariants
| Project/Area Number |
18540051
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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 | Nihon University |
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Principal Investigator |
TOMARI Masataka Nihon University, 文理学部, 教授 (60183878)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Keiichi 日本大学, 文理学部, 教授 (10087083)
MATSUURA Yutaka 日本大学, 文理学部, 准教授 (50096905)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | 代数幾何学 / 特異点 / ゴレンスタイン性 / 有理特異点 / 基本サイクル / 極大イデアルサイクル / ブロウイングアップ / 2次元星型特異点 / 重複度 / F-threshold / 単純K3特異点 / 非退化完全交差式 / 中心フィルトレーション / F-thresholds / 重複度予想 / 超曲面特異点 / simple K3特異点 / ニュートン境界 / フィルター付きブロウイングアップ / 幾何種数 / フロベニウス写像 / 特異点解消 / 代数的スタック / ベロネーゼ環 / 字数付き環 / exceptional log canonical singularity / 密着閉包 / stack |
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| Research Abstract |
Tomari found a sufficient condition for the new 5 classes of hypersurface simple K3 singularities would be the last of 95+5 classes. The four of these 5 classes are the classical one found in the Ishii-Tomari theory on Veronese subring of famous 95 classes, but the other one is completely new one. Watanabe has been studying F-threshold, integral closures, and tight closures of several ideals and got many results.
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Report
(6 results)
Research Products
(21 results)
