Strong F-regularity of all Hankel determinantal rings

Determine whether every Hankel determinantal ring over a field of positive characteristic is strongly F-regular.

Background

The paper studies test ideals and strong F-regularity for Hankel determinantal rings, which are quotients of polynomial rings by ideals generated by minors of Hankel matrices. The authors prove that the test ideal is the entire ring, and hence that the ring is strongly F-regular, when the defining ideal is generated by the determinant of a square Hankel matrix (the case t=m=n).

They also note that Hankel determinantal rings defined by 2×n Hankel matrices are Veronese subrings and therefore strongly F-regular in positive characteristic. A computational example for a 3×4 Hankel matrix likewise has unit test ideal. These results motivate the unresolved question of whether strong F-regularity holds for every Hankel determinantal ring.