2001 Fiscal Year Final Research Report Summary
Classification of higher dimensional hypersurface singularities in terms of nondegenerate complete intersections
Project/Area Number 
12640020

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Kanazawa University 
Principal Investigator 
TOMARI Masataka Kanazawa University, Faculty of sciences, Associate professor, 理学部, 助教授 (60183878)

CoInvestigator(Kenkyūbuntansha) 
KODAMA Akio Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (20111320)
ISHIMOTO Hiroyasu Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (90019472)
FUJIMOTO Hirotaka Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (60023595)
MORISHITA Masanori Kanazawa University, Faculty of sciences, Associate professor, 理学部, 助教授 (40242515)
HAYAKAWA Takayuki Kanazawa University, Graduate school of natural science and technology, Assistant, 自然科学研究科, 助手 (20198823)

Project Period (FY) 
2000 – 2001

Keywords  blowing up / multiplicity / isoloted singularity / rational singulerity / value distrilution theony / terminal singulauty / Milnor number / divisor class group 
Research Abstract 
On the main theme of this project : (1) In 2000, M. Tomari studied the nitration of ideals on terminal singularities where the associated graded rings are integral domains with isolated singularity. As a special case, he showed the regularity of their associated graded rings of 3dimensional regular local ring. In 1 2001, Tomari gave an inequality about Milnor number μ(f) of a hypersurface isolated singularity Uin terms of weighted Taylor expansion of the defining equation f. Here the equality holds iiand only if the initial form defines an isolated singularity. This gives a characterization of a semiquasihomogeneous condition in terms of μ. The proof uses a result of Tomari on multiplicity of filtered ring. (2) T. Hayakawa studied several partial resolutions of 3dimensipnal terminal singularities with index is not less than two. In 2000, he constructed an interesting example which admits a partial resolution where at worst Gorenstein terminal singularities remain. This was understood naturally by the' studies of the special partial resolution of rational double points which appears as the general members of anticanonical linear system of the singularity. In 2001 he also studied the irreducible components of this type of partial resolution. As relatedworks on complex analysis : (3) H. Fujimoto had succeeded to construct a new series of examples of hyperbolic hypersurfaces of degree 2^n in ndimensional complex protective spaces. In the case of n = 2, this example gives the world record of the minimal possible degree of the ambient spaces for such situation. (4) A. Kodama studied the general ellipsoids with not necessary smooth boundaries from the points of view of the Webster metric.

Research Products
(16 results)