The numerical Amitsur group

TL;DR

This paper introduces the numerical Amitsur group, an computable approximation of the Amitsur subgroup, and applies it to derive bounds and compute examples for toric varieties.

Contribution

It defines the numerical Amitsur group, enabling computation via Euler-Poincaré characteristic, and applies this to bound and compute Amitsur subgroups for certain varieties.

Findings

Established a uniform upper bound on the Amitsur subgroup exponent

Computed Amitsur subgroups for toric varieties

Demonstrated the numerical Amitsur group as an effective approximation

Abstract

The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup that can be computed using only the Euler-Poincar\'e characteristic on the Picard group. As an application, we find a uniform upper bound on the exponent of the Amitsur subgroup that depends only on the dimension and arithmetic genus of the variety and is independent of the group. Finally, we compute Amitsur subgroups of toric varieties using these ideas.