2005 Fiscal Year Final Research Report Summary
Lattices, automorphic forms and moduli spaces
| Project/Area Number |
14204001
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Nagoya University |
|---|
Principal Investigator |
KONDO Shigeyuki Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (50186847)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
UMEMURA Hiroshi Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (40022678)
TSUCHIYA Akihiro Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (90022673)
YOSHIKAWA Ken-ichi University of Tokyo, Graduate School of Mathematics, Associate Professor, 大学院・数理科学研究科, 助教授 (20242810)
FUJINO Osamu Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (60324711)
ITO Yukari Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 講師 (70285089)
|
|---|
| Project Period (FY) |
2002 – 2005
|
| Keywords | Moduli / Automorphic form / Del Pezzo surface / K3 surface |
|---|
| Research Abstract |
In this project we gave a description of the moduli space of del Pezzo surfaces as an arithmetic quotient of a complex ball by means of the theory of periods of K3 surfaces. By the same method, we showed that the moduli space of 8 points on the projective line can be written as an arithmetic quotient of 5-dimensional complex ball. Moreover we gave a relation of our description and the theory of complex reflection groups due to Deligne-Mostow. On the other hand, by using the theory of automorphic forms on a bounded symmetric domain of type IV, we gave a projective model of the moduli of 8 points on the projective line which coincides with the classical one defined by the cross ratio.
It is not well known that K3 surfaces in positive characteristic. In this project, we studied the most special supersingular K3 surface in characteristic 2. Also we gave a few new examples of supersingular K3 surfaces on which Mathieu groups of degree 11 and 22 act symplectic automorphisms.
|
