Lojasiewicz inequalities in a certain class of smooth functions

2023/11/06 by Lam, Ha Minh, Vui, Ha Huy
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.03298

Abstract

Let f be a germ of a smooth function at the orirgin in \RRⁿ. We show that if f is Kouchnirenko's nondegenerate and satisfies the so called Kamimoto--Nose condition then it admits the Łojasiewicz inequalities. We compute the Łojasiewicz exponents for some special cases. In particular, if f is a germ of a smooth convex Kouchnirenko's nondegenerate function and satisfies the Kamimoto--Nose condition, then all its Łojasiewicz exponents can be expressed very simply in terms of its Newton polyhedron.

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