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On a question of Teissier

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Abstract

Using a result of Demailly and Pham on log canonical thresholds, we give an upper bound for polar invariants from a question of Teissier on hypersurface singularities. This provides a weaker alternative upper bound compared to the one conjectured by Teissier.

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Notes

  1. This paper was written after we got interested from [12] and before the appearance of [10].

  2. But our method does not deal with the Arnold exponent directly. It will be interesting if the method of this paper can be further combined with the complex analytic aspect of the Arnold exponent = the minimal exponent.

  3. The same argument can be also checked using [4, Thm. 10.10] and the definition of \(\theta (f)\).

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Acknowledgements

The author is grateful to Mircea Mustaţǎ and Alexander Rashkovskii for helpful comments. This research was supported by Basic Science Research Program through NRF Korea funded by the Ministry of Education (2018R1D1A1B07049683).

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  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, Korea

    Dano Kim

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Kim, D. On a question of Teissier. Annali di Matematica 200, 2305–2311 (2021). https://doi.org/10.1007/s10231-021-01081-x

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