Project/Area Number  09640021 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Kanazawa University 
Principal Investigator 
TOMARI Masataka Graduate school of natural science and technology, Kanazawa University Associate professor, 自然科学研究科, 助教授 (60183878)

CoInvestigator(Kenkyūbuntansha) 
MORISHITA Masanori Fuculty of sciences, Associate professor, 理学部, 助教授 (40242515)
HAYAKAWA Takayuki Fuculty of sciences, Assistant, 理学部, 助手 (20198823)
KODAMA Akio Fuculty of sciences, Professor, 理学部, 教授 (20111320)
ISHIMOTO Hiroyasu Fuculty of sciences, Professor, 理学部, 教授 (90019472)
FUJIMOTO Hitotaka Fuculty of sciences, Professor, 理学部, 教授 (60023595)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1998 : ¥1,000,000 (Direct Cost : ¥1,000,000)
Fiscal Year 1997 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  the normal graded rings / rational singularities / weighted blowingups / conjecture of M.Reid / the Segre product / terminal singularities / the arithemetic genus / the special log forms / 正規次数付環 / 有理特異点 / 重みつきブローイングアップ / Reid予想の反例 / Segre積 / 端末特異点 / 特異点の算術種数 / 対数的微分形式 / ネバンリンナ理論 / 単純K3特異点 / 因子的ブロイングアップ / 正則曲線の一意性定理 / 多様体のホモトピー同値 / 正則自己同型群 / アデル幾何学 
Research Abstract 
On the main theme of this project : (1)In 1997, M.Tomari found more 3 examples of simple K3 singularities which do not belong to the famous 95 classess. It was a natural continuation of studies of previous year. Tomari also found a. counter example to an analogus conjecture of M.Reid about 4dimensional terminal singularities in terms of Newton boundary. In the both studies, the theory of filtered blowingup by TomariWatanabe plays an essential role. In 1998, Tomari succeeded to prove the criterion about the rational singularities and isolated singularities about the Segre product of two normal graded rings. The criterions are natural generalizations to those for the normal graded rings in terms of PinkhamDemazure's construction. (2)T.Hayakawa studied several partial resolutions of 3dimensional terminal singularities by weighted blowingups. In particular he succeded to show a special corespondence between the set of divisorial blowingups with minimal discrepancy and the set of the maximal blowingups with "big weight". He classified the elementary contraction with the minimal discrepancy in his situation. (3)M.Takamura gave a very good estiamte about the arithemetic genus of normal twodimensional singularities of multiplicity two in terms of the Horikawa canonical resolution. Combined with the previous result of Tomari, he obtained the complete classification of the case of p_<alpha> = 2. As related works on complex analysis : (4)K.Morita studied the special log forms which gives abasis of higher dimensional de Rham cohomology which is related to the arrangements of hyperfurface on the complex affine space. The work is aimed to give application to integral representaion of hypergeomeric functions of several variables and a natural generalization of AomotoKita's theory.
