2002 Fiscal Year Final Research Report Summary
Quasiprojectivity of moduli spaces of algebraic varieties
| Project/Area Number |
12640064
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
TSUJI Hajime Tokyo Institute of Technology, Department of Mathematics, Associate Professor, 大学院・理工学研究科, 助教授 (30172000)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
FUJITA Takao Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (40092324)
ISHII Shihoko Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (60202933)
FUTAKI Akito Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (90143247)
HATTORI Toshiaki Tokyo Institute of Technology, Department of Mathematics, Associate Professor, 大学院・理工学研究科, 助手 (30251599)
|
|---|
| Project Period (FY) |
2000 – 2002
|
| Keywords | moduli space / plurigera / vareiteis of general type / multiplier ideal sheaves |
|---|
| Research Abstract |
We proved that the quasiprojectivity of moduli spaces of nonsingular projective varieties in general.
It will appear as a joint paper with G.Schumacher (Annals of Mathematics 159).
I also proved that the deformation invariance of plurigenera for projective deformations of projective Manifolds. This is a very fundamental result in algebraic geometry.
Also I proved that there exsists a positive constant $nu_{n}$ such that for every $m geqq nu_{n}$ and every projective $n$-fold of general type $X$, $mK_{X}$ gives a birational embedding of $X$.
This is also very fundamental result in algebraic geometry.
|
