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.
我们通过最近发展的衍生投影和衍生膨胀理论的新视角,研究了嵌套颤振变种的二元几何。证明了对于任意套颤器(带环或不带环),两类套颤器变体是同构的,在导出对角线鼓化后,是同构的。给出了中岛颤振群上的量子环和环面代数作用的弱分类。在此基础上,我们还研究了拟光滑导出格式的去微分理论。我们证明了对于特征为0的情况,任何拟光滑的导出格式(嵌入到光滑的环境变量中),都允许通过导出的膨胀光滑中心进行去分辨。它允许我们对任何拟光滑的派生格式给出k理论虚基类的一个猜想。本研究揭示了范畴表征理论与两族几何和派生代数几何之间的惊人关系。它允许我们计算变体的更多对角分解(k -理论,Chow群或Fourier-Mukai变换),这对几何表示理论的研究至关重要。

项目成果

期刊论文数量(0)
专著数量(0)
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A CATEGORICAL QUANTUM TOROIDAL ACTION ON THE HILBERT SCHEMES
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Zhao Yu其他文献

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
Deterministic controlled-phase gate and SWAP gate with dipole induced transparency in the weak-coupling regime
弱耦合状态下具有偶极子诱导透明度的确定性控制相位门和交换门
  • DOI:
    10.1016/j.optcom.2016.05.054
  • 发表时间:
    2016
  • 期刊:
  • 影响因子:
    2.4
  • 作者:
    Liu A-Peng;Cheng Liu-Yong;Zhang Shou;Zhao Yu;Gao Xiao-Zhen;Chang Yan-Hong;Wang Ai-Ping
  • 通讯作者:
    Wang Ai-Ping
Microwave-Assisted Syntheses of 2′,3′- O -isopropylidene ribonucleoside 5′-monophosphates
微波辅助合成2′,3′-O-异丙叉核糖核苷5′-单磷酸酯
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
Experimental study on the composite fouling characteristics of calcium carbonate and nanometer magnesia
碳酸钙与纳米氧化镁复合污垢特性的实验研究

Zhao Yu的其他文献

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