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.
我们研究双有理几何的嵌套类簇,通过一个新的角度非常最近发展的理论,派生的投影和派生爆破。证明了对任意的环(有环或无环),两种套环簇同构,导出对角爆破后同构。在此基础上,我们还研究了拟光滑导方案的去奇异性理论。我们证明了,对于特征0的情况下,任何准光滑的衍生计划(嵌入到一个光滑的环境品种),允许一个程序的desingulization衍生爆破光滑中心。这一研究揭示了范畴表示理论、双有理几何和导出代数几何之间令人惊讶的联系。它允许我们计算更多的对角分解(K理论,周群或傅立叶-向井变换)的品种,这是至关重要的几何表示理论的研究。

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

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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