arXiv subjects
Publications and source records attributed to Grzegorz Oleksik.
We prove the constancy of the Łojasiewicz exponent in non-degenerate $μ$-constant deformations of surface singularities. This is a positive answer to a question posed by B. Teissier.
We give an algorithm to compute the Lê numbers of (the germ of) a Newton non-degenerate complex analytic function $f\colon(\mathbb{C}^n,0) \rightarrow (\mathbb{C},0)$ in terms of certain invariants attached to the Newton diagram of the function $f+z_1^{α_1}+\cdots +z_d^{α_d}$, where $d$ is the dimension of the critical locus of $f$ and $α_1,\ldots, α_d$ are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A. G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have the same Lê numbers.
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 [8]. It is also a multidimensional generalization of the Lenarcik theorem [13].