Perverse sheaves and schobers

反常的滑轮和 schobers

• 批准号: 20H01794
• 负责人: Bondal Alexey
• 金额: $ 10.9万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2020
• 资助国家: 日本
• 起止时间: 2020-04-01 至 2025-03-31
• 项目状态: 未结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20H01794/
• 关键词: schober; schobers; Derived categories; Floor theory; noncommutative; resolutions; Schober; Derived category; Perverse sheaves; Minimal Model Program; Algebraic varieties; coherent sheaf; derived category; complex manifold; Chern classes; qu

The principal investigator A. Bondal developed the theory of noncommutative resolutions in the geometric and algebraic contexts. Algebraic resolutions were constructed via generalized noncommutative differential calculus for a collection of algebras and homomorphisms between them. Noncommutative resolutions for non-normal algebraic varieties were constructed in collaboration with co-Investigator S. Okawa by means of the universal fibered and cofibered squares.Co-investigator M. Kapranov (in collaboration with V. Schechtman) explicitly described perverse sheaves on the Ran space of the complex line. The categorical interpretations of this construction was explored.Co-investigator S. Okawa proved that the category of coherent right modules over a smooth noncommutative surface finite over its center is equivalent to a direct summand of the category of coherent sheaves of a smooth tame algebraic stack, which is canonically associated to it, thereby confirming that such nc surfaces are noncommutative geometric schemes in the sense of Orlov. The paper on this results is submitted to the electronic arxive.As a byproduct of his research on sheaf-theoretic quantization co-investigator T.Kawasaki found a sheaf-theoretic version of the bounding cochain, which was known before in the context of Floer theory.

主要研究者A. Bondal在几何和代数背景下制定了非交通分辨率的理论。代数分辨率是通过广义的非交通差分计算构建的，以收集代数和同态。非正态代数品种的非共同分辨率与共同投资者S. Okawa合作，通过通用的纤维纤维和辅助方形。探索了这种结构的分类解释。注册申请者S. Okawa证明，在其中心上平稳的非交换表面有限的相干权利模块类别等于直接汇总的一类相干滑皮类别的类别相干的托架堆栈，这是驯服的态度，在此范围内，这是在此类别上与之相关的。奥洛夫的感觉。有关该结果的论文已提交给电子杂志。作为他对副理论量化的研究的副产品T.Kawasaki发现了边界Cochain的横扫理论版本，该版本以前在Floer理论的背景下众所周知。

项目成果

Flops and spherical functors

触发器和球形函子

• DOI: 10.1112/s0010437x22007497
• 发表时间: 2022
• 期刊: Compositio Mathematica
• 影响因子: 1.8
• 作者: Bodzenta Agnieszka;Bondal Alexey
• 通讯作者: Bondal Alexey

CURRENT TRENDS IN THE CATEGORICAL APPROACH TO ALGEBRAIC AND SYMPLECTIC GEOMETRY

代数和辛几何分类方法的当前趋势

• 发表时间: 2023

Derived categories of complex manifolds, their DG-enhancement and Bott-Chern classes

复流形的派生类别、它们的 DG 增强和 Bott-Chern 类

• 发表时间: 2022
• 作者: Ando S;Nishida A;Yamasaki S;Endo K;Hiraiwa-Hasegawa M;Kasai K.;Alexey Bondal
• 通讯作者: Alexey Bondal

Two derived categories of a generic complex torus

通用复环的两个派生类别

• 发表时间: 2022
• 作者: Tada Kanae;Ezaki Takahiro;Kondo Hirohito M.;Flanagan Brendan;小野崎優花・佐藤弘美・溝上陽子;Alexey Bondal
• 通讯作者: Alexey Bondal

Perverse sheaves and schobers on symmetric products3 Name of Conference

对称产品上的反常滑轮和肖伯斯3 会议名称

• 发表时间: 2022
• 作者: Takuma Iwasaki;Hiromi Sato;& Yoko Mizokami;Mikhail Kapranov
• 通讯作者: Mikhail Kapranov