| Project/Area Number |
15K04829
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kanagawa University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2018-03-31
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | 有限体 / 射影空間 / 超曲面 / Hermitian超曲面 / 射影代数幾何 / 平面代数曲線 / Sziklai予想 |
|---|
| Outline of Final Research Achievements |
This research project focused on the number of points of a hyper-surface in a certain projective space over a finite field.
In the previous project, we had shown, so-called, an `elementary bound' for hyper-surfaces of a fixed degree over a finite field in projective n-space, which is an upper bound of the number of rational points of hyper-surfaces without linear components, and, for n = 3, we had determined the all optimal surfaces in the sense of this bound.
In this project, we handled hyper-surfaces without singular points. For odd number n, we got an upper bound for the number of points of those hyper-surfaces, and settled the problem of finding all optimal hyper-surfaces in the sense of this bound.
|
