Complex symplectic varieties and derived categories

复辛簇和派生范畴

• 批准号: 15340008
• 负责人: NAMIKAWA Yoshinori
• 金额: $ 3.71万
• 依托单位: Osaka University (2005)Kyoto University (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340008/
• 关键词: derived categories; complex symplectic variety; deformation; Mukai flop; nilpotent orbit; birational geometry; Poisson変形; 変形理論; フロップ; 複素シンプレクティック多様性; シンプレクティック特異点; 複素単純リー環

1. Mukai flops : (a) We proved that there is an equivalence between derived categories under a Mukai flop. The equivalence is not obtained from the graph of the flop, but from the fiber product. But the same picture is no more true for a G(2,4) flop ; in other words, the functor obtained from the graph of the fiber product is not an equivalence. (b) The nilpotent orbit closure of Complex a simple Lie algebra is a symplectic singularity. All crepant resolutions of such singularities are obtained as the Springer resolutions. In general, the member of crepant resolutions of a singularity is greater than one. We proved that crepant resolutions of such a nilpotent orbit closure are described as a finite sequence of Mukai flops of type A, D and E_6.2. Deformations of singular symplectic varieties. We proved that, model the minimal under conjecture, the following are equivalent.(1) a projective symplectic variety Y has a crepant resolutions(2) a projective symplectic variety Y has a smoothing by a deformations

1。MukaiFlops：（a）我们证明了mukai flop下的派生类别之间存在等效性。等效性不是从翻牌的图中获得的，而是从纤维产物中获得的。但是对于g（2,4）flop而言，相同的图片不再如此。换句话说，从纤维产物图获得的函子不是等效性。 （b）复合物的nilpotent轨道闭合一个简单的谎言代数是一种象征性的奇异性。所有这种奇异性的毛茸茸的分辨率都是作为施普林格分辨率获得的。一般而言，奇异性的怪胎决议成员大于一个。我们证明了这种nilpotent轨道闭合的毛茸茸的分辨率被描述为A型，D和E_6.2的Mukai Flops的有限序列。奇异品种的变形。我们证明，模拟最小的猜想，以下是等效的。（1）射影符号变化y具有毛虫的分辨率（2）射影的符号变化y具有变形的平滑性y

项目成果

加藤 文元: "Rigid analytic geometry (Japanese)"数学,「論説」. 55. 392-417 (2003)

加藤文元：“刚性解析几何（日文）”，《数学》，《社论》55. 392-417（2003）。

Uniqueness of crepant resolutions and symplectic varieties

绉纹分辨率和辛簇的独特性

• 发表时间: 2004
• 期刊: Ann.Inst.Fourier 54
• 作者: B.Fu;Y.Namikawa
• 通讯作者: Y.Namikawa

Mukai flops and derived categories

Mukai 失败和派生类别

• 发表时间: 2003
• 期刊: J.reine, Angew.Math. 560
• 作者: H.Ohta;K.Ono;R.Goto;T.Mabuchi;T.Mabuchi;A.Fujiki;R.goto;T.Mabuchi;T.Mabuchi;A.Fujiki;Ryushi Goto;Y.Namikawa
• 通讯作者: Y.Namikawa

並河 良典: "Mukai flops and derived categories II"C.R.M.Proc.Series, AMS. (発表予定). (2004)

Yoshinori Namikawa：“Mukai flops 和衍生类别 II”C.R.M.Proc.Series，AMS（即将推出）。

Cornelissen, 加藤文元: "Equivariant deformation of Munford curves and of ordinary curves of positive characteristic"Duke Math.J.. 116. 431-470 (2003)

Cornelissen、Fumimoto Kato：“Munford 曲线和正特征普通曲线的等变变形”Duke Math.J.. 116. 431-470 (2003)