Geometry of autoequivalence groups via isometric actions on the space of stability conditions

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K22310
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Osaka University (2022); Chuo University (2020-2021)
• Principal Investigator: Kikuta Kohei 大阪大学, 大学院理学研究科, 助教 (10880073)
• Project Period (FY): 2020-09-11 – 2023-03-31
• Keywords: K3曲面 / 導来圏 / 自己同値群 / 安定性条件の空間 / 等長作用

Outline of Final Research Achievements

We studied autoequivalence groups of derived categories via (isometric) actions on the space of stability conditions. The main topics are as follows: Hochschild entropy, intersection number and spherical twists, constructions of rank 2 free subgroups, the center subgroups of autoequivalence groups for K3 surfaces, Thurston compactifications of the space of stability conditions for curves.

Free Research Field

代数幾何学，群論

Academic Significance and Societal Importance of the Research Achievements

代数多様体の自己同値群とは群と呼ばれる数学的対象の一種であり，物理学とも深く関わる導来圏の対称性を記述する．古くから研究されてきた自己同型群を自然に含み，純粋に群論の研究対象としても興味深い．本研究では，安定性条件の空間への群作用を考察することで，自己同値群に関する理解を深めることができた．