2003 Fiscal Year Final Research Report Summary
Behavior of discrete invariants of algebraic varieties under deformation
| Project/Area Number |
13640011
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
OGISO Keiji The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MATSUO Atsushi The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (20238968)
TERASOMA Tomohide The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (50192654)
KAWAMATA Yujiro The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 教授 (90126037)
KONDO Shigeyuki The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・多元数理研究科, 教授 (50186847)
YOSHIKAWA Kenichi The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (20242810)
|
|---|
| Project Period (FY) |
2001 – 2003
|
| Keywords | k3 surface / hyperkahler manifold / deformation / Picard number / Fourier-Mukai partner / auromorphism group / Mordel-Weil lattice / Kummer structure |
|---|
| Research Abstract |
The most important result of this project is that I have clarified the behavior of Picard numbers of hyperkahler manifolds under 1-dimensional small deformation and applied this to the following three results :
(1)Solution of the filling-up problem of Picard numbers of hyperkahler manifolds ;
(2)Coarse classification of the Mordell-Weil lattices of Jacobian K3 surfaces ;
(3)Clarification of the behavior of the automorphis groups of K3 surfaces under deformation.
Jointly with F. Catanese and J. H. Keum, I have also applied the result to the conjycture of De-QiZhang about the fundamental groups of normal K3 surfaces.
Jointly with S. Hosono, B. Lian and S. T. Yau, I have also obtained the explicit counting formula for the Fourier-Mukai partners of a K3 surface and applied this to the monodromy representation of the simplistic diffeomorphism groups of the mirror family of a K3 surface and T. Shioda's question about kummer structures of a K3 surface.
|
