The study of ideal limits of sequences of test configurations

2016 Fiscal Year Final Research Report

• Project/Area Number: 25610012
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Osaka University
• Principal Investigator: MABUCHI TOSHIKI 大阪大学, その他部局等, 名誉教授 (80116102)
• Co-Investigator(Renkei-kenkyūsha): NAKAGAWA Yasuhiro 佐賀大学, 大学院工学研究科, 教授 (90250662) ; NITTA Yasufumi 東京工業大学, 大学院理工学研究科, 助教 (90581596)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: テスト配位列 / K-安定性 / Donaldson-二木不変量 / polybalanced計量 / 相対安定性

Outline of Final Research Achievements

We made a systematic study of the completion of the moduli space of test configurations for a polarized algebraic mamifold. As a typical example of our study, we obtain the Donaldson-Futaki invariant for sequences of test configurations on a polarized algebraic manifold. This then allows us to introduce the concept of strong K-stability. Moreover, by a joint work with Nitta, we showed that strong K-stability implies asymptotic Chow stability. These results in particular give us various applications in the existence problem of extremal Kaehler metrics.

Free Research Field

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