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Inner jumping numbers of non-degenerate polynomials

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Abstract

The inner jumping numbers were introduced by Budur to relate two different measures of the complexity of the singularities of an effective divisor D on a nonsingular complex variety X: the jumping numbers of a pair (X,D) and the Hodge spectrum at a singular point of D. We give an elementary proof for an effective and combinatorial description of inner jumping numbers (\(<1\)) of non-degenerate polynomials.

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Notes

  1. If f has non-degenerate part (i.e. it is non-degenerate just with respect to its compact faces), then the same statement holds in a Zariski neighborhood of the origin.

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Acknowledgments

The author thanks Nero Budur, Mirel Caibăr and Anatoly Libgober for interesting discussions on the topic of this paper. The author also thanks Gary Kennedy for his help with the editing of the manuscript. This research was partially supported by MCI-Spain grant MTM2010-21740-C02.

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  1. Mathematics Center Heidelberg (MATCH), Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 288, 69120 , Heidelberg, Germany

    Manuel González Villa

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  1. Manuel González Villa
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Correspondence to Manuel González Villa.

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Villa, M.G. Inner jumping numbers of non-degenerate polynomials. Math. Z. 274, 1113–1118 (2013). https://doi.org/10.1007/s00209-012-1108-7

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  • DOI: https://doi.org/10.1007/s00209-012-1108-7

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