Quasiprojectivity of moduli spaces of algebraic varieties

代数簇模空间的拟射影

• 批准号: 12640064
• 负责人: TSUJI Hajime
• 金额: $ 1.66万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640064/
• 关键词: moduli space; plurigera; vareiteis of general type; multiplier ideal sheaves; 多重標準系; 劣随伴定理; Flip; 概代数性

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.

我们证明了通常与G.Schumacher的联合论文（数学159），我还证明，Plurigenera的变形不变性用于投影歧管的投影性不变。这是代数几何形状的一个非常基本的结果。我还证明了一个正常的$ nu_ {n} $，以至于每$ m geqq nu_ {n} $和每个投射$ n $ n $ fold $ n $ fold $ x $ x $ x $，$ mk_ {x} $ serement andials and $ x $ fime y seement is of $ x $。

项目成果

G.Schumacher, H.Tsuji: "Quasiprojectivity of Moduli Spaces of Polarized Varieties"Annals of Mathematics. (to appear).

G.Schumacher、H.Tsuji：“极化簇模空间的拟射影性”数学年鉴。

H.TSUJI: "Deformation invariance of plurigenera"Nagoya Math. J.. (掲載予定). (2002)

H.TSUJI：“多倍体的变形不变性”Nagoya Math J.（即将出版）。

Quasiprojectivity of moduli spaces of algebraic varieties

代数簇模空间的拟射影

• 发表时间: 2004
• 期刊: Annals of Math. 159(to appear)

Deformation invariance of plurigenera

多属植物的变形不变性

• 发表时间: 2002
• 期刊: Nagoya Math J. 166

H.Tsuji: "Deformation Invariance of Plural genera"Proc. of Hoyoma Symporlum 2000. (2001)

H.Tsuji：“复数属的变形不变性”Proc。