Resolution of singularities by using Newton polyhedra and its application to analysis

2020 Fiscal Year Final Research Report

• Project/Area Number: 15K04932
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: Kamimoto Joe 九州大学, 数理学研究院, 准教授 (90301374)
• Project Period (FY): 2015-04-01 – 2021-03-31
• Keywords: ニュートン多面体 / 特異点解消定理 / ベルグマン核 / ダンジェロの型 / 代数曲線 / 振動積分 / 局所ゼータ関数

Outline of Final Research Achievements

By using Newton polyhedra, which is an important concept in singularity theory,
we developed a quantitative resolution of singularities theorem. Furthermore, we apply the resolution theorem to several complex variables and harmonic analysis and obtain many kinds of interesting results. To be more specific, we obtain strong results about the analytic continuation of local zeta functions, asymptotic analysis of oscillatory integrals and determination of D'Angelo's types.

Free Research Field

多変数複素解析学

Academic Significance and Societal Importance of the Research Achievements

代数や幾何における重要な成果をさらに発展させ応用することにより、今までに十分でなかった解析学における重要な問題について、多くの成果を得たこと。