| Project/Area Number |
20540050
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
WATANABE Keichi Nihon University, 文理学部, 教授 (10087083)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TOMARI Masataka 日本大学, 文理学部, 教授 (60183878)
YOSHIDA Kennichi 名古屋大学, 多元数理研究科, 准教授 (80240802)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
FUKUDA Takuo 日本大学, 文理学部, 教授 (00009599)
KURANO Kazuhiko 明治大学, 理工学部, 教授 (90205188)
TAKAGI Shunsuke 九州大学, 大学院・理学研究科, 准教授 (40380670)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Keywords | 代数学 / 特異点論 / 可換環論 / 代数幾何学 / Frobenius写像 / F-threshold / 乗数イデアル / 整閉包 / 正標数の手法 / 次数付環 / 重複度 / test ideal / a-invariant / Gorenstein環 / coefficient ideal / lc threshold / 特異点 / 代数幾何 / jumping number |
|---|
| Research Abstract |
We investigated the property of singularities appearing in the minimal model theory in algebraic geometry. Specifically, we got the following results. 1. We introduced the notion of F-thresholds of pair of ideals and got a conjecture concerning F-threshold and multiplicity of ideals. We proved the conjecture in some important cases. 2. We gave a procedure to construct (quasi) Gorenstein graded rings with given a-invariant from normal projective varieties. 3. We investigated diagonal subalgebras of multi-graded rings and gave a criterion for such rings to be rational singularity. We also gave a new example concerning theory of divisor class groups.
|
