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在几何和代数的背景下发展了非交换分解理论。利用广义非交换微分构造了一组代数及其同态的代数分解。非正规代数簇的非交换分解是与共同研究者S。大川通过通用纤维和cofibered广场。Kapranov（与V. Schechtman合作）明确描述了复直线的Ran空间上的反常层。对这一结构的分类解释进行了探讨。Okawa证明了在中心有限的光滑非交换曲面上的凝聚右模范畴等价于光滑驯服代数栈的凝聚层范畴的直和项，这是与它正则相关的，从而证实了这样的nc曲面是奥尔洛夫意义下的非交换几何概型。关于这一结果的论文被提交给了电子arxive。作为他研究层理论量子化的副产品，合作研究者T.川崎发现了一个层理论版本的束缚上链，这在Floer理论的背景下是已知的。

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