Geometric structure of mixed non-degenerate singularity

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400098
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tokyo University of Science
• Principal Investigator: Oka Mutsuo 東京理科大学, 理学部, 教授 (40011697)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 混合多項式 / ミルナー束 / ニュートン境界 / ミルナーファイバー / レンズ方程式

Outline of Final Research Achievements

We clarrified the structure of Newton non-degenerate mixed singularities. In particular, we gave a formula for the zeta function of mixed function with strongly polar weighted face functions. We also showed the existence of the contact structure on such a link. We also showed the relation of the moduli space of strongly mixed homogeneous polynomials of two variables and the moduli of mixed polynomials of one variables and the range of possible number of roots.It is also shown that the Lens equation studied in astro-physics has strongly related to our moduli problem.

Free Research Field

特異点の幾何学