Research on singularities on an algebraic variety
Project/Area Number |
16K05089
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | The University of Tokyo (2018) Tokyo Woman's Christian University (2016-2017) |
Principal Investigator |
Ishii Shihoko 東京大学, 大学院数理科学研究科, 名誉教授 (60202933)
|
Research Collaborator |
Watanabe Kei-ichi
|
Project Period (FY) |
2016-04-01 – 2019-03-31
|
Project Status |
Completed (Fiscal Year 2018)
|
Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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Keywords | singularities / arc space / minimal log discrepancy / discrepancies / jet schemes / Biratinational geometry / Singularities / Jet schemes / Discrepancies / Biratinational geometry / 1. Singularities / 2. Jet schemes / 3. Discrepancies / 4. Birational geometry / 特異点 / ジェットスキーム / 弧空間 |
Outline of Final Research Achievements |
A non-smooth point on a variety is called a singularity. In order to study those singularities, we need good invariants. In this research, we introduce an invariant; Mather-Jacobian log discrepancy and study the properties of this invariant. This invariant is interpreted in terms of the arc space on singularities of a variety. Therefore, making use of it, we obtain Inversion of Adjunction for the base field of positive characteristic and finite determinacy for the M-J log discrepancy for surfaces of characteristic 0.
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Academic Significance and Societal Importance of the Research Achievements |
多様体が滑らかであれば,コホモロジーの消滅定理をはじめとして,色々な良い性質が成立し,多様体全体の様相がわかりやすいのであるが,特異点があるとそれがわかりにくくなる.特異点をよく知ることで,多様体の理解を深めようというのが本研究の意義である.この研究は数学的に意義があることはもちろん,特異点の不変数の一つである log canonical threshold が学習理論において,重要な役割を果たすことが知られていることからもわかるように,社会にとっても意義のあることである.
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Report
(4 results)
Research Products
(29 results)