Bounding symbolic powers via asymptotic multiplier ideals

We revisit a bound on symbolic powers found by Ein-Lazarsfeld-Smith and subsequently improved by Takagi-Yoshida. We show that the original argument of Ein-Lazarsfeld-Smith actually gives the same improvement. On the other hand, we show by examples that any further improvement based on the same technique appears unlikely. This is primarily an exposition; only some examples and remarks might be new.Comment: 10 pages. Primarily exposition. Originally written as appendix to lecture notes by Brian Harbourne. v2: Minor changes. v3: Final version, appeared in Ann. Univ. Pedagog. Crac. Stud. Mat

Kansas v. Glover and the Issue of Reasonable Suspicion

It is settled law that an officer may initiate a traffic stop when there is articulable and reasonable suspicion that the person stopped has committed, is committing, or is about to commit a crime. In Kansas v. Glover, the Supreme Court has an opportunity to clarify what constitutes “reasonable suspicion.” The Court will determine whether it is reasonable for an officer to seize a vehicle if the registered owner has a revoked license and there is no information to suggest that the person driving is not the owner of the car. This Commentary argues that the Court should uphold the Kansas Supreme Court decision and find that the burden of reasonable suspicion was not met. Glover turns on whether the fact that a vehicle is registered to someone with a revoked license is enough to warrant reasonable suspicion. This Commentary posits that, in this instance, the State did not meet its burden as it relied on one questionable factor that was not based on an officer’s training. More generally, common sense and the Court’s own precedent support the idea that the State needs more justification to pull over a vehicle than the mere fact it is registered to someone with a suspended or revoked license. The current standard for reasonable suspicion is so slight that there is no need to lower it further, and the increase in public safety that would result from this less demanding standard is outweighed by the social costs of increased traffic stops