2009 Fiscal Year Final Research Report
Research on the singularities of a variety
| Project/Area Number |
18340004
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
ISHII Shihoko Tokyo Institute of Technology, 大学院・理工学研究科, 教授 (60202933)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TOMARI Masataka 日本大学, 文理学部, 教授 (60183878)
FUJITA Takao 東京工業大学, 大学院・理工学研究科, 教授 (40092324)
WATANABE Keiichi 日本大学, 文理学部, 教授 (10087083)
TOMARU Tadashi 群馬大学, 医学部, 教授 (70132579)
|
|---|
| Project Period (FY) |
2006 – 2009
|
| Keywords | 特異点 / 弧空間 / ジェットスキーム / 双有理幾何学 |
|---|
| Research Abstract |
We clarified the relationship between some properties of singularities on a variety and the properties on the arc space and the jet schemes over the variety. We gave a characterization of the regularity of the base variety by the flatness of a truncation morphism of jet schemes. The relationship between degenerating families of algebraic curves and two dimensional singularities. We introduced F-threshold for pair of ideals in commutative rings by means of positive characteristic method and generalized the formula on multiplicity.
|
