講演者

岡 睦雄氏（東京理科大学）

with Christophe Eyral (Polish Academy of Sciences)

会場

数学研究室1（埼玉大学理工学研究科棟5階）

アブストラクト

Let f(z1, . . . , zn) be a weighted homogeneous polynomial of degree d under a weight vector P = t(p1, . . . , pn). If f has an isolated singularity at the origin, Orlik-Milnor gave a beautiful formula for the Milnor number μ. We consider a polynomial g(z) = f(z) + h(z) such that f is a weighted homogeneous polynomial of degree d with one dimensional singularity at the origin and h is a polynomial with degP h = d + m, m ≥ 1 such that S(f) ∩ {hP } = {0} so that g has an isolated singularity at the origin. For homogeneous polynomials with m = 1, Luengo studied such singularities and gave a formula for its Milnor number. For m ≥ 2, Lˆe and Yomdin generalized the formula of Luengo, and for generic weighted homogeneous polynomial with n = 3, Artal Bartolo gave a formula for Milnor number. In this talk, we generalize these formulae for higher dimension. In this talk, I will explain first A’Campo formula for zeta function, Varchenko formula and then explain our formula as an application of almost Newton non-degenerate functions.