  In this note I give a description of Lyubeznik's local cohomology invariants
for a certain natural class of local rings, namely the ones which have the same
local cohomology vanishing as one expects from an isolated singularity. This
strengthens the results of Bondu and myself in math.AG/0406265 while at the
same time somewhat simplifying the proofs. Through examples I further point out
the bad behavior of these invariants under reduction to positive
characteristic.
