Graded families of ideals and convex regions

2026/07/26 by Haoxi Hu
#math.AC #math.AG #math.CO

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Abstract

We study the interplay between graded families of ideals in \mathbbK-domains and their associated convex regions. These regions, called Newton-Okounkov regions, arise naturally from graded families of ideals associated to a valuation with one-dimensional leaves. Our main focus is to compute asymptotic resurgence number of a pair of graded families of ideals. By combining techniques from Attouch--Wets topology and convex-geometric properties of Newton-Okounkov regions, we characterize the asymptotic resurgence number through containment relations between the pair of corresponding Newton-Okounkov regions.

Citations

• Resurgence number of graded families of ideals
• Duality for asymptotic invariants of graded families
• Newton-Okounkov body, Rees algebra, and analytic spread of graded families of monomial ideals
• On the resurgence and asymptotic resurgence of homogeneous ideals
• Demailly's Conjecture and the Containment Problem
• Chudnovsky's Conjecture and the stable Harbourne-Huneke containment
• Asymptotic resurgence via integral closures
• Multiplicities Associated to Graded Families of Ideals
• Asymptotic resurgences for ideals of positive dimensional subschemes of\n projective space
• Comparing powers and symbolic powers of ideals
• Symbolic powers of monomial ideals and vertex cover algebras

Related

• Resurgence number and convex body associated to pairs of graded families of ideals
• Resurgence number of graded families of ideals
• Convex bodies and multiplicities of ideals
• Local Okounkov bodies and limits in prime characteristic
• Asymptotic resurgence via integral closures