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The Łojasiewicz exponent of nondegenerate surface singularities
Part of
Szymon Brzostowski, Tadeusz Krasiński, Grzegorz Oleksik
Journal:

Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023

Published online by Cambridge University Press:

26 June 2023, pp. 1391-1410

Print publication:

December 2023
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Let f be an isolated singularity at the origin of $\mathbb {C}^n$. One of many invariants that can be associated with f is its Łojasiewicz exponent $\mathcal {L}_0 (f)$, which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for $\mathcal {L}_0 (f)$ in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates.