Categorical Representation Theory on an Algebraic Surface

代数曲面上的分类表示论

基本信息

  • 批准号:
    22K13889
  • 负责人:
  • 金额:
    $ 1.83万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Early-Career Scientists
  • 财政年份:
    2022
  • 资助国家:
    日本
  • 起止时间:
    2022-04-01 至 2025-03-31
  • 项目状态:
    未结题

项目摘要

We study the birational geometry of nested quiver varieties, through a new perspective of very recent developed theories of derived projectivizations and derived blow-ups. We prove that for any quiver (with or without loops), two kinds of nested quiver varieties are isomorphic, after derived blowing-up the diagonals, are isomorphic. It leads to a weak categorification of the quantum loop and toroidal algebras action on the Grothendieck group of Nakajima quiver varieties.After that, we also studied the desingulization theory of quasi-smooth derived schemes. We proved that for the characteristic 0 case, any quasi-smooth derived schemes (with an embedding into a smooth ambient variety), allows a procedure of desingulization by derived blowing up smooth centers. It allowed us to formulate a conjecture of K-theoretic virtual fundmanetal classes for any quasi-smooth derived schemes.This study revealed the surprising relation among the categorical representation theory, birational geometry and derived algebraic geometry. It allows us to compute more diagonal decomposition (K-theoretic, Chow groups or Fourier-Mukai transforms) of varieties, which is crucial to the study of geometry representation theory.
通过最近发展起来的派生射影和派生爆破理论的新视角,我们研究了嵌套箭图变种的双生几何。证明了对于任一箭图(有环或无环),两类嵌套箭图簇同构,导出爆破对角线后,两类嵌套箭图簇同构。在此基础上,对Nakajima箭图的Grothendieck群上的量子环和环状代数作用进行了弱分类,并研究了拟光滑衍生格式的去奇化理论。我们证明了对于特征为0的情形,任何拟光滑的导出格式(嵌入到光滑的环境簇中)都允许通过爆破光滑中心来去奇异。这项研究揭示了范畴表示理论、二元几何和派生代数几何之间惊人的联系。它允许我们计算更多的簇的对角分解(K-理论、Chow群或Fourier-Mukai变换),这对于几何表示理论的研究是至关重要的。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES
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Zhao Yu其他文献

Sodium taurocholate-dependent lipid efflux by ABCA1-Four-step model for HDL formation-
ABCA1 牛磺胆酸钠依赖性脂质流出-HDL 形成的四步模型-
  • DOI:
  • 发表时间:
    2009
  • 期刊:
  • 影响因子:
    0
  • 作者:
    長尾耕治郎;Zhao Yu;木村泰久;植田和光
  • 通讯作者:
    植田和光
Multi-task encoder with attention mechanism to remove noise from GPR signal
具有注意机制的多任务编码器可消除探地雷达信号中的噪声
  • DOI:
    10.1117/12.2673896
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Dongying Li;Zhao Yu;Chongpeng Tian;Da Yuan
  • 通讯作者:
    Da Yuan
Copper nanoclusters-based fluorescent sensor array to identify metal ions and dissolved organic matter.
基于铜纳米簇的荧光传感器阵列,用于识别金属离子和溶解的有机物。
  • DOI:
    10.1016/j.jhazmat.2021.128158
  • 发表时间:
    2022-01
  • 期刊:
  • 影响因子:
    13.6
  • 作者:
    Xu Jinming;Zhou Huangmei;Zhang Yixue;Zhao Yu;Yuan Hao;He Xiaoxiao;Wu Ying;Zhang Sanjun
  • 通讯作者:
    Zhang Sanjun
The current status of compassion factors in oncology nurses and influencing factors
Tape casting fabrication and properties of planar waveguide YAG/Yb:YAG/YAG transparent ceramics
平面波导YAG/Yb:YAG/YAG透明陶瓷的流延制备及性能
  • DOI:
    10.1016/j.optmat.2017.04.032
  • 发表时间:
    2017-07
  • 期刊:
  • 影响因子:
    3.9
  • 作者:
    Zhao Yu;Liu Qiang;Ge Lin;Wang Chao;Li Wenxue;Yang Chao;Wang Juntao;Yuan Lei;Xie Tengfei;Kou Huamin;Pan Yubai;Gao Qingsong;Bo Yong;Peng Qinjun;Xu Zuyan;Li Jiang
  • 通讯作者:
    Li Jiang

Zhao Yu的其他文献

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