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Computing jumping numbers in higher dimensions

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Abstract

The aim of this paper is to generalize the algorithm to compute jumping numbers on rational surfaces described in Alberich-Carramiñana et al. (Mich Math J 65(2):287320, 2016) to varieties of dimension at least 3. Therefore, we introduce the notion of \(\pi \)-antieffective divisors, generalizing antinef divisors. Using these divisors, we present a way to find a small subset of the ‘classical’ candidate jumping numbers of an ideal, containing all the jumping numbers. Moreover, many of these numbers are automatically jumping numbers, and in many other cases, it can be easily checked.

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Authors and Affiliations

  1. Department of Mathematics, KU Leuven, Celestijnenlaan 200B, Box 2400, 3001, Leuven, Belgium

    Hans Baumers

  2. Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany

    Ferran Dachs-Cadefau

Authors
  1. Hans Baumers
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  2. Ferran Dachs-Cadefau
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Corresponding author

Correspondence to Ferran Dachs-Cadefau.

Additional information

The first author was supported by a Ph.D. fellowship of the Research Foundation—Flanders (FWO). The second author is partially supported by Spanish Ministerio de Economía y Competitividad MTM2015-69135-P.

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Baumers, H., Dachs-Cadefau, F. Computing jumping numbers in higher dimensions. manuscripta math. 161, 35–59 (2020). https://doi.org/10.1007/s00229-018-1069-1

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