Poincaré series of multiplier and test ideals

• Josep Àlvarez Montaner ^[1] ; Luis Núñez-Betancourt ^[2]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
  2. [2] Mathematics Research Center

     Mathematics Research Center

     México

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 6, 2022, págs. 1993-2009
• Idioma: inglés
• DOI: 10.4171/RMI/1347
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• Resumen

  • 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 R which gives a unified treatment of both cases