so there was a question on the putnam recently that to an algebraic geometer is naturally phrased in terms of the variety parameterizing tuples (A, M, B) of nxn matrices such that AM = MB and A and B have the same characteristic polynomial. it was tempting to prove the desired result by showing that the subset of such tuples where M is invertible is zariski dense, but i couldn't show that and ended up doing something else. any thoughts?
