Project/Area Number 
14540017

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Nihon University (2003) Kanazawa University (2002) 
Principal Investigator 
TOMARI Masataka Nihon University, College of Humanities ad Sciences, Professor, 文理学部, 教授 (60183878)

CoInvestigator(Kenkyūbuntansha) 
WATANABE Keiichi Nihon University, College of Humanities ad Sciences, Professor, 文理学部, 教授 (10087083)
IWASE Zjunichi KANAZAWA University, Graduate School of Natural Science and Technology, Assistant, 大学院・自然科学研究科, 助手 (70183746)
HAYAKAWA Takayuki KANAZAWA University, Graduate School of Natural Science and Technology, Assistant, 大学院・自然科学研究科, 助手 (20198823)
FUKUDA Takuo Nihon University, College of Humanities ad Sciences, Professor, 文理学部, 教授 (00009599)
MATSUURA Yutaka Nihon University, College of Humanities ad Sciences, Associate Professor, 文理学部, 助教授 (50096905)
児玉 秋雄 金沢大学, 理学部, 教授 (20111320)
加須栄 篤 金沢大学, 理学部, 教授 (40152657)
菅野 孝史 金沢大学, 理学部, 教授 (30183841)

Project Period (FY) 
2002 – 2003

Project Status 
Completed (Fiscal Year 2003)

Budget Amount *help 
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥2,100,000 (Direct Cost: ¥2,100,000)

Keywords  resolution of singularities / filtered blowingup / plurigenus / 3dimensional terminal singularities / Gluck surgery / algebraic stacks / order function of local rings / associated graded rings / フィルター付ブロウイングアップ / フリップの存存定理 / 双正則同形問題 / 4次元多様体 / Dehn手術 
Research Abstract 
On our research, the following results are given. Some of these were alreadypublished, and the rest will be published soon. (1)The head investigator Tomari showed; (a) By the theory of multiplicy of filtered rings, a new proof of characterization of 2dim, regular local ring was given. (b) There are new progress for the study of lower bound of L^2 plurigenus from the point of views concerning the tangent cone of the filtration. A characterization of the equality in the above had done. (c) Seeking for a future progress to extend the results of (b), he introduced L^2 plurigenus for 1dim singularities. Using a technique of filtered blowingup, he gave a classification of 1dim, singularities by the asymptotic behavior of this L^2 genus as in the same way as higher dim, cases. This is an evidence to extend the studies of (b) in more general situations. (d) Also he made a progress concerning linear complementary inequality about the order functions on normal 2dim, singularities of multip
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licity two. (e) Combining recent results by T. Okuma, Tomari gave a geometric characterization of normal 2dim. Gorenstein elliptic singularities, which was conjectured about 20 years ago by Tomari. Through these studies, all the investigators of this project contributed in several forms. Among others, Hayakawa and Iwase had been contacting to Tomari and giving many contributions in these periods. Further, as related subjects of the project, there are several individual results as follows; (2) In the minimal model theory, Hayakawa classified all the 3dim. extremal contractions to one point, where the discrepancy is less than one. (3) Iwase continued the studies of a kind of Gluck surgery of 4dim, manifold, and showed the all cases become the Dehn surgery along torus as same as 3dim, studies. (4) Matsuura gave a criterion of affine properties of algebraic stacks ; which has been interested by algebraic geometers in many years. (5) Watanabe made several essential progress about the relations between integral closed ideals and multiplier ideals. Less
