2017 Fiscal Year Final Research Report
Commutative Ring Theory of Singularities
| Project/Area Number |
26400053
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nihon University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
吉田 健一 日本大学, 文理学部, 教授 (80240802)
|
|---|
| Project Period (FY) |
2014-04-01 – 2018-03-31
|
| Keywords | Singularity / Local rings / surface singularity / integrally closed ideals / log resolution / rational singularity / elliptic singularity / Gorenstein ring |
|---|
| Outline of Final Research Achievements |
The singularities in algebraic geometry is described by commutative ring theory. Conversely, the geometric properties of a singularities;arity effects properties of the corresponding commutative ring and thus we can construct many examples of rings via geometric data. In this research, we focused on isolated singularities of algebraic surfaces and studies the properties of singularities by looking at integrally closed ideals of the singularity. In particular, the discovery of concept of "p_g-ideal is a big success of our research.
On the other hand, we used the method of analyzing singularities in characteristic 0 by the aid of commutative ring theory of positive characteristic, so called "F-Singularities". We could get some new properties of Hilbert-Kunz multiplicities.
|
| Free Research Field |
数物系科学
|
