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.

首席研究员A. Bondal在几何和代数环境中发展了非交换分辨率理论。利用广义非交换微分学，构造了一组代数及其同态的代数解析。与合作研究者S. Okawa合作，利用通用纤维平方和协纤维平方构造了非正代数变量的非交换分辨。共同研究者M. Kapranov（与V. Schechtman合作）明确地描述了复线的Ran空间上的反常轴。对这种结构的分类解释进行了探讨。共同研究者S. Okawa证明了中心有限的光滑非交换曲面上的相干右模的范畴等价于与之正则相关的光滑代数堆上的相干束的范畴的直接和，从而证实了这样的曲面是Orlov意义上的非交换几何格式。关于这一结果的论文已提交给电子档案馆。作为他对束理论量子化研究的副产品，共同研究者川崎发现了束理论版本的边界协链，这是在弗洛尔理论的背景下已知的。

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

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

The PROB of graded bialgebras, perverse sheaves on configuration spaces and Hecke algebroids

分级双代数、构形空间上的反常滑轮和 Hecke 代数体的 PROB

• 发表时间: 2022
• 作者: Majumdar Rwitajit;Bakilapadavu Geetha;Rajendran Ramkumar;Sahasrabudhe Sameer;Flanagan Brendan;Chen Mei-Rong Alice;Ogata Hiroaki;Mikhail Kapranov
• 通讯作者: Mikhail Kapranov

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