The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface

2008/06/02 by Carlos Galindo, Galindo, Carlos, Francisco Monserrat +1 · 1 citation
Computer Science · Mathematics · #13H05 #14B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0806.0231

openalex publication_date 2008/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a simple complete ideal \wp of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincaré series P_\wp, that gathers in an unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to \wp. This paper is devoted to prove that P_\wp is a rational function giving an explicit expression for it.

Cited by

• Quasi-ordinary hypersurfaces, multiplier ideals and local tropicalizations

Related

• Poincar 'e series of multiplier ideals in two-dimensional local rings\n with rational singularities
• Poincaré series of multiplier and test ideals
• Jumping Coefficients of Multiplier Ideals
• Multiplicities of jumping points for mixed multiplier ideals
• The Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational