Work

Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals

Year: 2026

Type: preprint

Abstract: This work concerns ideals invariant under the action of the group of linear base changes on a generic matrix; we call these GL-invariant ideals. We determine the ordinary powers, their saturations with respect to determinantal ideals, and the symbolic powers of GL-invariant ideals. We give explicit formulas for asymptotic invariants known as (skew) Waldschmidt constants and asymptotic resurgence, which measure the growth of these families and compare the ordinary and symbolic topologies. We also prove that the generalized symbolic Rees algebras associated with these ideals are Noetherian.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.03131

Authors: Bisui, Sankhaneel, Seceleanu, Alexandra

Institution: University of Nebraska–Lincoln

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Alfred P. Sloan Foundation, Division of Mathematical Sciences

Awards: Mathematical Sciences Research Institute (MSRI), G329468232, Polynomial Interpolation, Symmetric Ideals, and Lefschetz Properties, G4663222005, G4972001970, G6019427330, G7692653605

OpenAlex ID: W7208717657

Cites: 2

Cited by:

Related to: 10