Ben Blum-Smith

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20242026

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math.AC2026

Geometry of numbers and degree bounds for rational invariants

Ben Blum-Smith, Sylvan Crane, Karla Guzman +2

We investigate degree bounds for fields of rational invariants of representations of finite groups. We prove many cases of a bound for $Z / p Z$ conjectured by Blum-…

math.AC2025

Generic orbits, normal bases, and generation degree for fields of rational invariants

Ben Blum-Smith, Harm Derksen

For a faithful linear representation $V$ of a finite group $G$ in coprime characteristic, we show that if the field Noether number $β_{field}$ is the minimum $d$ such that…

math.AC2024

Degree bounds for rational generators of invariant fields of finite abelian groups

Ben Blum-Smith

We study degree bounds on rational but not necessarily polynomial generators for the field $k (V)^{G}$ of rational invariants of a linear action of a finite abelian group. We…