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- W1518562009 abstract "Let f : ( C n , 0 ) → ( C , 0 ) be a semiquasihomogeneous function. We give a formula for the local Łojasiewicz exponent L 0 ( f ) of f, in terms of weights of f. In particular, in the case of a quasihomogeneous (QH) isolated singularity f, we generalize a formula for L 0 ( f ) of Krasiński, Oleksik and Płoski from 3 to n dimensions. This was previously announced in the paper [19] of Tan, Yau and Zuo [Łojasiewicz inequality for weighted homogeneous polynomial with isolated singularity, Proc. Amer. Math. Soc. 138 (2010) 3975–3984], but as a matter of fact it was not proved correctly there, as noted by the AMS reviewer Tadeusz Krasiński. As a consequence of our result, we obtain that the Łojasiewicz exponent is invariant in topologically trivial families of singularities coming from a QH germ. This is an affirmative partial answer to Teissier's conjecture." @default.
- W1518562009 created "2016-06-24" @default.
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- W1518562009 date "2015-09-18" @default.
- W1518562009 modified "2023-09-23" @default.
- W1518562009 title "The Łojasiewicz exponent of semiquasihomogeneous singularities" @default.
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- W1518562009 doi "https://doi.org/10.1112/blms/bdv058" @default.
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