Abstract. We give an explicit formula for the ̷ Lojasiewicz exponent of an isolated weighted homogeneous surface singularity in terms of its weights. From the formula we get that the ̷ Lojasiewicz exponent is a topological invariant of these singularities.
In the article we give some estimations of the Łojasiewicz exponent of nondegenerate surface singularities in terms of their Newton diagrams. We also give an exact formula for the Łojasiewicz exponent of such singularities in some special cases. The results are stronger than Fukui inequality [F]. It is also a multidimensional generalization of the Lenarcik theorem [L].
In this article we give a su‰cient and necessary condition for a Kouchnirenko nondegenerate holomorphic function to have an isolated singularity at 0 in terms of its support. As a corollary we give some useful su‰cient conditions for singularity to be isolated.
In this paper, we present a conjecture connecting the Łojasiewicz exponent of an isolated nondegenerate singularity with some geometrical characteristics of the Newton diagram associated with this singularity. We prove the conjecture for a class of surface singularities.
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