Discreteness and rationality of F-jumping numbers on singular varieties

2009/06/30 by Manuel Blickle, Karl Schwede, Shunsuke Takagi +1 · 6 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.AG #msc:13A35 #msc:14B05

paper · pdf · doi:10.1007/s00208-009-0461-2

published as Mathematische Annalen, Volume 347, Number 4, 917-949, 2010 · 29 pages, minor changes, to appear in Mathematische Annalen

arxiv created 2009/10/13 · openalex publication_date 2009/12/11 · arxiv updated 2010/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove that the F-jumping numbers of the test ideal τ(X; Δ, \ba^t) are discrete and rational under the assumptions that X is a normal and F-finite variety over a field of positive characteristic p, K_X+Δ is \bQ-Cartier of index not divisible p, and either X is essentially of finite type over a field or the sheaf of ideals \ba is locally principal. This is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero.

Cited by

• Test ideals via algebras of p^-e-linear maps
• Limit F -signature functions of two-variable binomial hypersurfaces
• On strongly F-regular inversion of adjunction
• Limit F-signature functions of two-variable binomial hypersurfaces
• Discreteness of 𝐹-jumping numbers at isolated non-ℚ-Gorenstein points
• On the behavior of test ideals under finite morphisms

Related

• On the discreteness and rationality of F-jumping coefficients
• Jumping Coefficients of Multiplier Ideals
• Jumping Numbers on Algebraic Surfaces with Rational Singularities
• Poincar 'e series of multiplier ideals in two-dimensional local rings\n with rational singularities
• Computing jumping numbers in higher dimensions