2011 Fiscal Year Final Research Report
Homological Mirror Symmetry of Isolated Hypersurface Singularities With Group Actions
| Project/Area Number |
20684003
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Osaka University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 幾何学 / 代数学 / 数理物理学 / ミラー対称性 |
|---|
| Research Abstract |
Based on the idea of the Mirror symmetry which interchanges the role of the algebra and the geometry, three kinds of triangulated categories are associated to the algebra, the representation theory and the geometry. Looking at some properties of these triangulated categories, we show that the" Arnold' s strange duality" is now naturally understood as a mirror symmetry between orbifold curves and cusp singularities with group action, which is generalized to an infinite series of singularities.
|
