Ben Blum-Smith

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math.AC2026

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 $I^_{field}^{2}$ is the minimum $d$ such tha…

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.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…

math.AC2024

Degree bounds for fields of rational invariants of $Z / p Z$ and other finite groups

Ben Blum-Smith, Thays Garcia, Rawin Hidalgo +1

Degree bounds for algebra generators of invariant rings are a topic of longstanding interest in invariant theory. We study the analogous question for field generators for the field…

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

Geometry of numbers and degree bounds for rational invariants

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

Degree bounds for fields of rational invariants of Z/pZ and other finite groups

Degree bounds for fields of rational invariants of $Z / p Z$ and other finite groups