Zariski-Nagata Theorems for Singularities and the Uniform Izumi-Rees Property

2024/06/02 by Polstra, Thomas · 2 citations
#13A30 #13H15 (Primary) 13A18 #14C17 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.00759

Abstract

We introduce and explore the Uniform Izumi-Rees Property in Noetherian rings with applications to multiplicity theory and containment relationships among symbolic powers of ideals. As an application, we prove that if R is a normal domain essentially of finite type over a field, there exists a constant C so that for all prime ideals \mathfrakp⊆ \mathfrakq\inSpec(R), if \mathfrakp⊆ \mathfrakq^(t), then for all n∈ℕ, there is a containment of symbolic powers \mathfrakp^(Cn)⊆ \mathfrakq^(tn).

Cited by

• On the uniform positivity of F-signature under reduction modulo p
• Degree functions of graded families of ideals

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• Comparing powers and symbolic powers of ideals
• Symbolic power containments in singular rings in positive characteristic
• Rational symbolic powers of ideals
• Strong F-regularity and the Uniform Symbolic Topology Property
• Symbolic powers of ideals defining F-pure and strongly F-regular rings