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Yano’s conjecture

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Abstract

We present a proof of a conjecture proposed by Yano (Sci Rep Saitama Univ Ser 10(2): 21–28, 1982) about the generic \( b \)-exponents of irreducible plane curve singularities.

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Notes

  1. It is enough to take \( r \) small enough so that the cycles constructed in Sect. 13 lie on \( \overline{X}_{i, t}\).

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Acknowledgements

The author would like to thank his advisors, Maria Alberich-Carramiñana and Josep Àlvarez Montaner, for the fruitful discussions, the helpful comments and suggestions, and the constant support during the development of this work. The author would also like to thank Ben Lichtin for providing many helpful comments on a first draft of this work.

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  1. Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium

    Guillem Blanco

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The author was supported by the grants Ministerio de Economía y Competitividad MTM2015-69135-P, Generalitat de Catalunya 2017SGR-932 and Agencia Estatal de Investigación PID2019-103849GB-I00. The author is supported by a Postdoctoral Fellowship of the Research Foundation – Flanders.

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Blanco, G. Yano’s conjecture. Invent. math. 226, 421–465 (2021). https://doi.org/10.1007/s00222-021-01052-2

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