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. Mukai flops：（a）证明了在Mukai flops下，导出范畴之间存在等价性。等价性不是从随角异色的图形中得到的，而是从纤维积中得到的。但同样的画面对G（2，4）翻转不再正确;换句话说，从纤维积的图中得到的函子不是等价的。(b)复单李代数的幂零轨道闭包是辛奇点.所有这些奇异点的临界解都是作为Springer解得到的。一般来说，奇点的临界分解的成员大于1。我们证明了这样一个幂零轨道闭包的可分解性可描述为A、D和E_6型Mukai触发器的有限序列。奇异辛簇的变形。我们证明了，在猜想下的极小模型，以下是等价的。(1)一个射影辛簇Y具有一个可分解性;（2）一个射影辛簇Y具有一个形变光滑性

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）。

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

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

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)