Study of termination of flips

2023 Fiscal Year Final Research Report

• Project/Area Number: 19KK0345
• Research Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research (A))
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: The University of Tokyo
• Principal Investigator: GONGYO Yoshinori 東京大学, 大学院数理科学研究科, 教授 (70634210)
• Project Period (FY): 2019 – 2023
• Keywords: MMP / アバンダンス予想

Outline of Final Research Achievements

During the first few months of my stay in Salt Lake City, I had very good discussions with C. Hacon and others on the log version of Maximil variation, a-log canonical threshold, and termination of flips. After that, the United States also declared a state of emergency, and while I was in Salt Lake City, we had to repeat discussions via Zoom. However, we had many discussions on the abundance conjecture and related extension theorems. I also got some ideas on the termination problem of flips.

Free Research Field

代数幾何学

Academic Significance and Societal Importance of the Research Achievements

フリップの停止問題やアバンダンス予想は重要な未解決問題であり、その解決は他分野での応用への影響も大きい。そういう意味でも重要な部分の研究を仕事をしていると自負している。またその解決に向けて派生する問題もたくさんあり、それが代数幾何学自体の発展につながると思う。