JournalsrmiVol. 38, No. 6pp. 1993–2009

Poincaré series of multiplier and test ideals

  • Josep Àlvarez Montaner

    Universitat Politècnica de Catalunya; Centre de Recerca Matemàtica (CRM), Barcelona, Spain

  • Luis Núñez-Betancourt

    Centro de Investigación en Matemáticas, Guanajuato, Gto., Mexico
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Abstract

We prove the rationality of the Poincaré series of multiplier ideals in any dimension thus extending the main results for surfaces of Galindo and Monserrat and Alberich-Carramiñana et al. Our results also hold for Poincaré series of test ideals. In order to do so, we introduce a theory of Hilbert functions indexed over which gives a unified treatment of both cases.

Cite this article

Josep Àlvarez Montaner, Luis Núñez-Betancourt, Poincaré series of multiplier and test ideals. Rev. Mat. Iberoam. 38 (2022), no. 6, pp. 1993–2009

DOI 10.4171/RMI/1347