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
- 来源:
- 关键词:
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
- DOI:10.1017/s1474748022000585
- 发表时间:2020-09
- 期刊:
- 影响因子:0.9
- 作者:Yu Zhao
- 通讯作者:Yu Zhao
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
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
- DOI:
10.1080/10426500701807707 - 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
Wang Zhe;Zhao Yu - 通讯作者:
Zhao Yu
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
- DOI:
10.1007/s12206-017-1251-5 - 发表时间:
2018-01 - 期刊:
- 影响因子:1.6
- 作者:
Xu Zhiming;Wang Jingtao;Han Zhimin;Zhao Yu - 通讯作者:
Zhao Yu
Zhao Yu的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}