Poincar 'e series of multiplier ideals in two-dimensional local rings\n with rational singularities

2014/12/11 by Maria Alberich‐Carramiñana, Josep Álvarez Montaner, Alberich-Carramiñana, Maria +5
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1412.3607

openalex publication_date 2014/12/11 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study the multiplicity of the jumping numbers of an mathfrak m-primary\nideal mathfrak a in a two-dimensional local ring with a rational\nsingularity. The formula we provide for the multiplicities leads to a very\nsimple and efficient method to detect whether a given rational number is a\njumping number. We also give an explicit description of the Poincar 'e series\nof multiplier ideals associated to mathfrak a proving, in particular, that\nit is a rational function.\n

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