Multiplier Ideals of Sufficiently General Polynomials

2003/03/17 by Jason Howald, Howald, Jason · 2 citations
Computer Science · Mathematics · #14M25 14Q99 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.AG #msc:14M25 #msc:14Q99

paper · pdf · doi:10.48550/arxiv.math/0303203

9 pages, 1 figure

arxiv created 2003/03/17 · openalex publication_date 2003/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is well known that the multiplier ideal \multrI of an ideal I determines in a straightforward way the multiplier ideal \multrf of a sufficiently general element f of I. We give an explicit condition on a polynomial f ∈ \CC[x₁,...,x_n] which guarantees that it is a sufficiently general element of the most natural associated monomial ideal, the ideal generated by its terms. This allows us to directly calculate the multiplier ideal \multrf (for all r) of ``most'' polynomials f.

Cited by

• A tower of complete moduli spaces of Calabi-Yau n-folds
• Quasi-ordinary hypersurfaces, multiplier ideals and local tropicalizations

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