The h-vector of a ladder determinantal ring cogenerated by 2x2 minors is log-concave

Determinantal Schemes and Pure O-sequences

We prove that if a standard determinantal scheme is level, then its h-vector is a log-concave pure O-sequence, and conjecture that the converse also holds. Among other cases, we prove the conjecture in codimension two, or when the entries of the corresponding degree matrix are positive. We also find formulae for the h-vector in terms of the degree matrix.