Łojasiewicz exponents of non-degenerate holomorohic and mixed functions

2017/04/21 by Oka, Mutsuo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.06379

Abstract

We consider Łojasiewicz inequalities for a non-degenerate holomorphic function with an isolated singularity at the origin. We give an explicit estimation of the Łojasiewicz exponent in a slightly weaker form than the assertion in Fukui.For a weighted homogeneous polynomial, we give a better estimation in the form which is conjectured by Brzostowski, Krasinski and Oleksik under under some condition (the Łojasiewicz non-degeneracy). We also introduce Łojasiewicz inequality for strongly non-degenerate mixed functions and generalize this estimation for mixed functions.

Related

• Łojasiewicz exponents of a certain analytic functions
• The Łojasiewicz Exponent of Semiquasihomogeneous Singularities
• The Łojasiewicz exponent for weighted homogeneous polynomial with isolated singularity
• Lojasiewicz inequalities in a certain class of smooth functions
• The Lojasiewicz exponent for weighted homogeneous polynomials of two\n real variables