2011 Fiscal Year Final Research Report
Study of singularities in the minimal model theory in higher dimension
| Project/Area Number |
20684002
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 極小モデル理論 / 極小対数的食違い係数 / モチーフ積分 / イデアル進位相 / 昇鎖律 |
|---|
| Research Abstract |
I reduced the boundedness of minimal log discrepancies to the boundedness of multiplicities or embedding dimensions by using Riemann-Roch theorem, and through the analysis of Artinian rings as hyperplane sections, I recovered this boundedness in dimension 3 and the characterisation of 3-fold Gorenstein terminal singularities. From the point of view of the ascending chain condition, I studied the extension of the ideal-adic semi-continuity of log canonical thresholds due to Kollar and de Fernex, Ein, Mustata, to minimal log discrepancies, and proved this semi-continuity in the setting of purely log terminal singularities by using the theory of motivic integration. I studied also the classification of 3-fold divisorial contractions.
|
