Poincaré series of multiplier and test ideals

2021/02/16 by Montaner, Josep Àlvarez, Núñez-Betancourt, Luis
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.08024

Abstract

We prove the rationality of the Poincaré series of multiplier ideals in any dimension and 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 an unified treatment of both cases.

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