F-thresholds and Generalized test ideals of determinantal ideals of maximal minors

Abstract: We study higher jumping numbers and generalized test ideals associated to determinantal ideals over a field of positive characteristic. We work in positive characteristic and give a complete characterization of both families for ideals generated by maximal minors; and make a conjecture for the general case. Although these invariants are understood asymptotically - as their positive characteristic grows to infinity they essentially coincide with their characteristic zero analogues - there are known examples where the behavior in positive characteristic differs significantly from that of characteristic zero. This new knowledge associated to determinantal ideals strengthens the case that test ideals and multiplier exhibit essentially the same description even in small characteristics. We conjecture that a similar result holds for determinantal ideals of arbitrary size.