Abstract
This is an extended abstract with some of the results that will appear in the forthcoming paper [3] in which we prove the rationality of the Poincaré series associated to multipliers and test ideals as long as we have discreteness and rationality of the corresponding jumping numbers and Skoda’s theorem is available. In order to do so we extend the theory of Hilbert functions to the case of filtrations indexed over the rational numbers.
JAM is partially supported by Generalitat de Catalunya 2017SGR-932 project and Spanish Ministerio de Economía y Competitividad MTM2015-69135-P. LNB is partially supported by CONACYT Grant 284598 and Cátedras Marcos Moshinsky.
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Àlvarez Montaner, J., Núñez-Betancourt, L. (2021). \(\mathbb {Q}\)-Hilbert Functions of Multiplier and Test Ideals. In: Alberich-Carramiñana, M., Blanco, G., Gálvez Carrillo, I., Garrote-López, M., Miranda, E. (eds) Extended Abstracts GEOMVAP 2019. Trends in Mathematics(), vol 15. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-84800-2_1
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