2013 Fiscal Year Final Research Report
Applications of Frobenius splitting to algebraic geometry
| Project/Area Number |
23740024
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
TAKAGI Shunsuke 東京大学, 数理(科)学研究科(研究院), 准教授 (40380670)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 可換環論 / 代数幾何学 / フロベニウス分裂 / F特異点 |
|---|
| Research Abstract |
The goal of this research project was to give an affirmative answer to Schwede-Smith's conjecture, which says that a projective variety X over an algebraically closed field of characteristic zero is log Fano if and only if its modulo p reduction is globally F-regular for sufficiently large p. We proved that the conjecture holds true when X is a Mori dream space or a surface. Under the same assumption, that is, when X is a Mori dream space or a surface, we also proved that if its modulo p reduction is globally F-split for infinitely many p, then X is log Calabi-Yau.
|
Research Products
(18 results)
